Mumbai University Solved Question Papers
Logic 1
Previous Year Question Paper with Solution
BLS LLB 5 Years · Sem 1
2023-24 - ATKT 60/40 Examination
munotes.in
Mumbai
BLS LLB 5 Years Sem 1 Logic 1 2023-24 - ATKT 60/40 Question Paper with Solutions
MU law student group
Free to join
First published on munotes.in on 10 August 2026.
Published by munotes.in, Mumbai.
Model answers written and edited by the munotes.in editorial desk.
Passages from this volume may be quoted, in print, online or by an AI system, with credit: name munotes.in and link to this volume's page. The volume may not be reproduced as a whole. Full terms at munotes.in/content-license.
munotes.in is an independent study resource for students of the University of Mumbai. It is not affiliated with the University of Mumbai, and is not endorsed by it.
The University does not publish an official answer key for this paper. The answers in this volume are model answers, written to show how a full-mark answer is built. They are a study aid, not an authority on what an examiner marked.
The question paper reproduced here is the paper as set by the University of Mumbai at the 2023-24 - ATKT 60/40 examination.
Contents
The questions below are the paper as the University of Mumbai set it at the 2023-24 - ATKT 60/40 examination, in the order it was set.
MarksPage
MarksPage
The Paper as Set
The questions in this volume are the questions asked at the 2023-24 - ATKT 60/40 examination, reproduced as the University of Mumbai set them, in the order it set them. Nothing has been reworded, added or left out. Only the answers are ours. See the original question paper.
Duration 2 hours · Total marks 60 · 22 questions answered
How to use this volume
Solve the paper first, under exam conditions and against the clock. Then read the answers here and mark your own. Reading a solution before attempting the question feels productive and teaches very little, because recognising an answer is not the same as being able to write one.
SECTION I
Q.1) Answer the following in one or two sentences
any six · (12 marks)
1.State the rule of Excluded Middle with an example.[2]
Answer
The Law of Excluded Middle is the third of the three laws of thought. It states that everything must either be or not be: between a proposition and its denial there is no third possibility.
p v ~p, or "everything is either A or not-A"
Example: an agreement either is void or is not void. There is no middle state between the two, and no third thing it could be instead.
2.What is the quantity of A proposition? Give an example.[2]
Answer
The quantity of an A proposition is UNIVERSAL. The A proposition is the universal affirmative: the predicate is affirmed of the whole of the subject.
All S is P
Example: "All advocates are graduates."
Quantity answers the question how much of the subject is spoken of, and a universal speaks of every member of the subject class. Quality answers whether the copula joins or separates, and in an A proposition it joins, which is why the form is universal affirmative.
3.Discuss any one purpose of definition.[2]
Answer
One purpose, and the primary one: a definition fixes the meaning of a term and so removes ambiguity.
An argument in which a key word shifts its sense between the premise and the conclusion proves nothing; the mistake is the fallacy of equivocation, and a definition is what prevents it. By stating the attributes a thing must possess before the term applies, the definition anchors the word to one meaning for the whole of the discussion.
Example: most everyday disputes are verbal, that is, the parties agree on the facts and use a word differently. A quarrel about whether a colleague was "rude" ends the moment "rude" is defined, or turns out to be a real disagreement after all.
4.What is the difference between an antecedent and a consequent in a conditional statement?[2]
Answer
In a conditional or hypothetical statement of the form "If p, then q":
- The antecedent is the if-clause, p, the condition on which the assertion depends.
- The consequent is the then-clause, q, what is asserted to follow if the condition holds.
Example: in "If a person commits theft, then he is punishable", the antecedent is "a person commits theft" and the consequent is "he is punishable".
⚠️ Neither is asserted by itself. The statement does not claim that anyone has committed theft, nor that anyone is punishable; it asserts only the connection between the two.
5.Define 'statement.' Provide an example.[2]
Answer
A statement is a sentence that is either true or false, and no sentence which is neither is a statement. It is the unit that logic works on, and in most modern textbooks the word is used interchangeably with proposition.
Example: "Delhi is the capital of India." This is a statement, and it is true.
By contrast, "Is Delhi the capital of India?", "Go to Delhi" and "If only I were in Delhi" are all perfectly good sentences and none of them is a statement, because a question, a command and a wish assert nothing and so are neither true nor false.
6.Explain the concept of denotation.[2]
Answer
The denotation, or extension, of a term is the range of individuals or classes to which the term applies.
Examples: the denotation of "man" is Rama, Shyam, Fatima and every other human being; the denotation of "triangle" is equilateral, isosceles and scalene triangles; the denotation of "contract" is sale, lease, agency and bailment.
It is contrasted with the connotation, or intension, which is the sum of the essential attributes the term implies. Denotation is what the word covers; connotation is what it means.
7.Give the distribution of terms in 'A' proposition.[2]
Answer
In an A proposition, "All S is P":
- The subject is DISTRIBUTED.
- The predicate is UNDISTRIBUTED.
A term is distributed when the proposition speaks of every member of the class it names.
Example: in "All men are mortal", the proposition speaks of every man, so "men" is distributed. It does not speak of every mortal; it says only that the men are somewhere among the mortals, so "mortal" is undistributed.
8.What is meant by weak disjuncts? Give an example.[2]
Answer
A disjunction is weak, or inclusive, when it asserts that at least one of its alternatives is true and leaves open the possibility that both are. The alternatives are the disjuncts.
Symbol: p v q. False in one case only, where both disjuncts are false.
Example: "Candidates who are graduates or have three years of experience may apply." A graduate who also has three years of experience is not disqualified, so the "or" is weak.
It is contrasted with a strong or exclusive disjunction, which asserts one but not both, written (p v q) · ~(p · q). Example: "The accused is either guilty or innocent."
9.Identify the kind of other immediate inference. A dog is an animal. Big dog is a big animal.[2]
Answer
This is an immediate inference by ADDED DETERMINANT, and as it stands it is INVALID.
An inference by added determinant adds the same qualifying word to both the subject and the predicate of a proposition. It is valid only where the added word means exactly the same in both places.
Here it does not. "Big" is a relative term: what counts as big is fixed by the class it qualifies. A big dog is big for a dog, and it is a very small animal indeed set beside an elephant or a whale. The determinant therefore changes its meaning between the two occurrences, which breaks the Law of Identity, and the inference fails.
A valid instance of the same form: "A dog is an animal, therefore a black dog is a black animal." Black means the same thing in both places, and the inference holds.
10.Define 'Proposition'.[2]
Answer
A proposition is a statement in which something is affirmed or denied of something else, and which is therefore necessarily either true or false.
It has three parts: the subject, that about which something is asserted; the predicate, that which is asserted of it; and the copula, the part which joins the two and asserts or denies the relation.
Example: in "All men are mortal", "men" is the subject, "mortal" the predicate and "are" the copula.
SECTION II
Q.2) Write short notes on any two
12 marks
11.Deductive and inductive inferences.[6]
Answer
For full marks, cover: inference and its two divisions; each kind defined with an example; the table of differences; the kinds of induction; the connection between the two, which is what distinguishes a good answer; and the legal application.
Inference and its divisions
Inference is the mental process by which the mind passes from one or more propositions, the premises, to another, the conclusion. It is divided by the number of premises into immediate and mediate, and by the kind of support into deductive and inductive. This note is about the second division.
Deductive inference
The conclusion follows necessarily from the premises, so that it can never be wider than they are. If the premises are true, the conclusion must be true.
All men are mortal. Socrates is a man. Therefore Socrates is mortal.
Inductive inference
From a number of observed particular instances a general conclusion is drawn which goes beyond the evidence and is therefore only probable.
This crow is black, and that one, and that one. Therefore all crows are black.
The differences
| Point | Deductive | Inductive |
|---|---|---|
| Movement | General to particular | Particular to general |
| Conclusion | Follows necessarily | Probable only |
| Scope | Never wider than the premises | Always wider |
| New knowledge | Adds none about the world | Adds new knowledge |
| Basis | The relation of implication | Uniformity of nature and causation |
| Judged as | Valid or invalid | Strong or weak |
| One contrary instance | Does not arise | Destroys the generalisation |
| Founder | Aristotle | Bacon and Mill |
The kinds of induction
- Perfect induction: every instance of a closed class is examined, so the conclusion is certain and adds nothing.
- Induction by simple enumeration: a run of agreeing instances with no contrary one observed. Probable only, and one exception destroys it.
- Scientific induction: a causal connection established by observation and experiment, using Mill's methods.
The connection
They are not rivals. Induction supplies the general premises deduction reasons from, since "all men are mortal" is itself an induction. Deduction supplies the form in which induction is stated and tested, since Mill's methods are general rules applied to instances exactly as a major premise is applied to a minor. Scientific method runs both in one cycle: observation, induction to a hypothesis, deduction of its consequences, and experiment to test them.
Legal application
The judgment is deductive: rule of law as major premise, facts found as minor, order as conclusion. Finding the facts is inductive: a conclusion on circumstantial evidence is an induction from particulars, and the conditions in Sharad Birdhichand Sarda v State of Maharashtra AIR 1984 SC 1622 are Mill's method of elimination in judicial dress. A single judgment therefore runs the two in series.
12.Proposition and sentence.[6]
Answer
For full marks, cover: both definitions; the kinds of sentence that are not propositions; the table of differences; the two directions of the many-to-one relation; the third term, judgement; and why logic reduces sentences to logical form.
Sentence
A sentence is a grammatical unit: a group of words complete in itself as an expression of thought. Grammar divides sentences into assertive, interrogative, imperative, optative and exclamatory.
Proposition
A proposition is a statement in which something is affirmed or denied of something else, and which is therefore either true or false. It has three parts: subject, predicate and copula.
Only one kind of sentence expresses a proposition
| Sentence | Kind | A proposition? |
|---|---|---|
| All men are mortal. | assertive | Yes |
| Are all men mortal? | interrogative | No, it asks |
| Run! | imperative | No, it commands |
| May you live long. | optative | No, it wishes |
| What a fall was there! | exclamatory | No, it exclaims |
Every proposition is expressed in a sentence, but not every sentence expresses a proposition.
The differences
| Point | Sentence | Proposition |
|---|---|---|
| Belongs to | Grammar | Logic |
| Nature | A form of words | What those words assert |
| Parts | Subject and predicate, grammatically | Subject, predicate and copula, as terms |
| Truth value | Only the assertive kind has one | Always true or false |
| Word order | Fixed by the idiom of the language | Fixed by logical form |
The relation runs both ways
One proposition may be expressed by many sentences. "Rama killed Ravana" and "Ravana was killed by Rama" are two sentences and one proposition, and a Marathi translation is a third sentence and still the same proposition.
One sentence may express different propositions on different occasions, through ambiguity, or because it contains a word such as "I", "here" or "now" whose reference changes with the speaker.
The third term: judgement
A judgement is the mental act of affirming or denying; the proposition is that act expressed; the sentence is the grammatical clothing the expression wears. Judgement belongs to psychology, proposition to logic, sentence to grammar.
13.Singular Proposition in Traditional logic and its distribution of terms.[6]
Answer
For full marks, cover: the definition with examples; the difficulty it creates for a scheme built on quantity; how traditional logic solved it and why; the distribution that follows, affirmative and negative; the objection to the solution; the consequences for opposition; and the modern treatment.
What a singular proposition is
A singular proposition is one whose subject is a single definite individual, named or otherwise picked out.
Examples: "Socrates is wise"; "The Taj Mahal is a monument"; "This contract is void"; "The present Chief Justice of India is a woman."
The difficulty
The fourfold scheme A, E, I, O rests on quantity, that is, on how much of the subject class is spoken of, universal or particular. A singular proposition has no quantity in that sense at all: its subject is not a class with some members spoken of and others not, but one individual, spoken of entirely.
Traditional logic could not simply set such propositions aside, because they are the commonest propositions in ordinary use and because the syllogism needs them: "All men are mortal; Socrates is a man; therefore Socrates is mortal" is unusable if the minor premise has no place in the scheme.
The traditional solution
Traditional logic treats a singular proposition as UNIVERSAL.
The reason given is that in a universal proposition the predicate is affirmed or denied of the whole of the subject, and in a singular proposition it is affirmed or denied of the whole of the subject too, since the subject is one individual and nothing of it is left out. On that reasoning "Socrates is wise" behaves as an A proposition and "Socrates is not wise" as an E.
The distribution that follows
Once the proposition is classed as universal, distribution follows from the ordinary rule, universals distribute the subject and negatives distribute the predicate:
| Singular proposition | Treated as | Subject | Predicate |
|---|---|---|---|
| Socrates is wise | A | distributed | undistributed |
| Socrates is not wise | E | distributed | distributed |
The subject of every singular proposition is distributed, affirmative or negative, because the whole of it is spoken of. The predicate is distributed only where the proposition is negative, for the ordinary reason: to shut Socrates out of the class of wise beings is to shut him out of every member of it.
The objection
The solution is a convention adopted for the syllogism, and it is not an analysis. The tell is what it does to opposition. If "Socrates is wise" is an A proposition and "Socrates is not wise" an E, the two are contraries, and contraries may both be false; but these two plainly cannot both be false, since Socrates is either wise or not. So the classification gives the wrong answer about the very propositions it is applied to.
The modern treatment
Modern logic drops the difficulty rather than solving it. A singular proposition is written Wa, a predicate with an individual constant, and its denial ~Wa. No quantifier appears, so no question of quantity arises, and the two are simple contradictories, which is the right answer. Nor is distribution needed, because the rules that use it belong to the syllogism, and modern logic tests arguments by other means.
14.Obversion.[6]
Answer
For full marks, cover: the definition; the two operations it performs; the table for all four forms with worked examples; why it never fails; the rule about the contradictory term; the place of obversion in the compound eductions; and the caution about ordinary-language negatives.
The definition
Obversion is a form of eduction, that is, of immediate inference, in which the quality of the proposition is changed and the predicate is replaced by its contradictory, the meaning remaining exactly the same.
The original proposition is the obvertend; the inferred proposition is the obverse.
The two operations
- Change the quality, affirmative to negative or negative to affirmative. The quantity is not touched.
- Replace the predicate by its contradictory, P by non-P.
The two changes cancel each other in meaning, which is why the obverse says exactly what the obvertend said.
The table, with examples
| Form | Obvertend | Obverse | Example |
|---|---|---|---|
| A | All S is P | E: No S is non-P | All men are mortal → No men are non-mortal |
| E | No S is P | A: All S is non-P | No horses are bipeds → All horses are non-bipeds |
| I | Some S is P | O: Some S is not non-P | Some men are honest → Some men are not non-honest |
| O | Some S is not P | I: Some S is non-P | Some men are not wise → Some men are non-wise |
Obversion is valid for all four forms, which no other eduction is.
Why it never fails
The governing rule of all eduction is that no term may be distributed in the inferred proposition unless it was distributed in the original. Conversion runs into that rule because it moves the terms: the predicate becomes the subject, and its distribution may change.
Obversion moves nothing. The subject stays the subject and the predicate stays the predicate; only the quality changes and the predicate is negated. The subject's distribution is therefore untouched, and the predicate's distribution changes exactly as the change of quality requires, since an affirmative never distributes its predicate and a negative always does. Nothing can go wrong, and nothing does.
The rule about the contradictory
⛔ The new predicate must be the contradictory of the old one, never its contrary.
The obverse of "All swans are white" is "No swans are non-white". Writing "No swans are black" would be a contrary term and would assert far less, since non-white covers grey, brown and every other shade.
Its place among the eductions
Obversion is the workhorse from which the compound eductions are built:
- Contraposition = obvert, then convert. Add a second obversion for the full form.
- Inversion = for an A proposition, obvert, convert, obvert, convert by limitation.
Because obversion never fails, the point at which a compound eduction breaks down is always a conversion step, which is why an I proposition has no contrapositive and neither I nor O has an inverse.
SECTION III
Q.3) Solve any two questions
12 marks
15.a) Reduce the following sentences into logical form and identify and name distributed term or terms, giving reasons.[6]
- (i) Jackfruits are never green.
- (ii) Some women gossip.
- (iii) Few roses are red.
Answer
Strict logical form and the distribution rule
A proposition is in strict logical form when it reads
quantity sign + subject term + copula (is or are, present tense) + predicate term
| Form | Proposition | Subject | Predicate |
|---|---|---|---|
| A | All S is P | distributed | undistributed |
| E | No S is P | distributed | distributed |
| I | Some S is P | undistributed | undistributed |
| O | Some S is not P | undistributed | distributed |
Universals distribute the subject; negatives distribute the predicate.
(i) Jackfruits are never green.
No jackfruits are green things. (E proposition)
Distributed: both terms.
Reason: "never" is a universal sign of time, and what is denied at all times of the subject is denied of the whole of it. The proposition is therefore universal, and the "not" implicit in "never" attaches to the copula, so it is negative. An E proposition distributes its subject because the whole of it is spoken of, and its predicate because to shut the subject out of a class is to shut it out of every member of that class.
(ii) Some women gossip.
Some women are persons who gossip. (I proposition)
Distributed: neither term.
Reason: "some" is the plain particular sign. The finite verb "gossip" is split into the copula "are" and a predicate term, because in strict logical form the copula must be the bare verb "to be" in the present tense. Being particular the subject is undistributed, and being affirmative the predicate is undistributed too.
(iii) Few roses are red.
Some roses are not red things. (O proposition)
Distributed: the predicate, "red things", only.
Reason: "Few" is not "a few". "A few S are P" is affirmative and means that some are; "Few S are P" carries a negative force, meaning not many, that is, that most are not. The proposition is therefore a particular negative, and a negative distributes its predicate.
16.b) i) Construct a truth table for the following compound proposition: "I will either go for a movie or eat an ice cream."[6]
- (ii) Identify and symbolise the following simple propositions.
- (1) Sachin Tendulkar is a great cricketer.
- (2) Shyam is taller than Ravi.
- (3) Taj Mahal is beautiful.
Answer
(i) "I will either go for a movie or eat an ice cream"
Identification: a compound proposition; the connective is disjunction, signalled by "either ... or".
- Let p = I will go for a movie.
- Let q = I will eat an ice cream.
Symbolic form: p v q
The components are called disjuncts. Taken in the weak or inclusive sense, which is the sense logic fixes for the symbol, the proposition asserts that at least one of the two will happen and leaves open that both may.
Truth table
| p | q | p v q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Reading of the table: a disjunction is false in one case only, where both disjuncts are false. Here the statement is falsified only by a person who neither goes to the film nor eats the ice cream.
Which sense is meant here. Nothing prevents a person from doing both, so the inclusive reading is the natural one and the table above is the answer. Had the alternatives been mutually exclusive by their nature, as in "the accused is either guilty or innocent", the sense would be strong and the symbolisation would be (p v q) · ~(p · q), which is false on the first row as well.
(ii) Identify and symbolise the following simple propositions
1. Sachin Tendulkar is a great cricketer.
A singular proposition, that is, a class-membership proposition: a predicate attributed to a named individual, so no quantifier is used.
Gs, where G = "... is a great cricketer" and s = Sachin Tendulkar.
2. Shyam is taller than Ravi.
A relational proposition: it asserts a relation between two individuals rather than a quality of one.
Tsr, where T = "... is taller than ...", s = Shyam and r = Ravi.
The order matters, since Tsr and Trs say opposite things. The relation "taller than" is asymmetrical and transitive.
3. Taj Mahal is beautiful.
A singular proposition, again class-membership.
Bt, where B = "... is beautiful" and t = the Taj Mahal.
17.c) Identify the following modern definitions and provide reasons for your analysis.[6]
- (i) According to oxford dictionary a dot is a spot.
- (ii) An elephant is an animal that is seen in jungle.
- (iii) To be a pain in the neck means to be irritating.
Answer
The kinds of definition to choose from
By technique. Denotative: by example, by enumeration, ostensive. Connotative: synonymous, operational, genus and difference. By purpose: stipulative, lexical, precising, theoretical, persuasive.
(i) According to Oxford Dictionary a dot is a spot.
Kind: a lexical definition, given by the synonymous technique. No fallacy, so far as it goes.
Reasons: it is lexical because it reports the meaning the word already has in the language, which is what a dictionary does, and a lexical definition can therefore be true or false: it is right if that is how the word is used and wrong if it is not. Its technique is synonymous, one word given by another of the same meaning.
Its limit: a synonymous definition helps only a reader who already knows the other word, and it analyses nothing, so it states no genus and no differentia. Note also that the appeal to the dictionary settles usage and nothing else: a dictionary is an authority on how a word is used, not on what the thing is.
(ii) An elephant is an animal that is seen in jungle.
Kind: an attempted definition by genus and difference. It is defective: too wide, and the differentia is an accident.
Reasons: the genus, "animal", is correct. The supposed differentia, "seen in jungle", is not a differentia at all: tigers, deer, monkeys and a thousand other animals are seen in jungles, so the definition covers far more than the term and fails convertibility in one direction. Worse, being seen in a jungle is an accident of elephants and not part of their essence, since an elephant in a zoo is no less an elephant.
Corrected: an elephant is a large herbivorous mammal with a trunk, tusks and thick grey skin, which states attributes that belong to elephants always and to nothing else.
(iii) To be a pain in the neck means to be irritating.
Kind: a lexical definition of an idiom, given by the synonymous technique. No fallacy.
Reasons: the definiendum is itself a figure of speech, and the definiens is literal. That is the opposite of the fault the rules warn against: the rule forbids defining in figurative language, and here a figurative expression is being explained in plain language, which is exactly what it needs.
It remains a nominal definition, of a phrase and not of a thing: it tells a reader what English speakers mean by the idiom and analyses no essence, because an idiom has none to analyse.
18.d) Evaluate the following divisions. Give Reasons.[6]
- (i) Foods classified into fruits, vegetables, grains, and proteins.
- (ii) Sports divided into team sports, individual sports, extreme sports, and endurance sports.
- (iii) Education segmented into primary, secondary, tertiary, and vocational education.
Answer
The rules of logical division
- Only one fundamentum divisionis at each step; breach is cross-division.
- The members must be mutually exclusive.
- The division must be exhaustive.
- It must proceed step by step; breach is the saltus in dividendo.
- Every member must be a species of the genus divided.
All three divisions below break the first rule, in three different ways.
(i) Foods classified into fruits, vegetables, grains, and proteins.
Fallacy: cross-division, and the members overlap.
Reasons: fruits, vegetables and grains divide food by its botanical or culinary kind; "proteins" divides it by nutrient content. Two bases at one step, so rule 1 is broken. Rule 2 falls with it, because a grain such as wheat is also a source of protein and a pulse is at once a vegetable and a protein, so one item belongs to two members. The list is also not exhaustive, since meat, fish, dairy and fats are foods and appear under no member as a kind.
(ii) Sports divided into team sports, individual sports, extreme sports, and endurance sports.
Fallacy: cross-division, and the members overlap badly.
Reasons: three bases are at work. Team and individual divide sports by the number of participants; "extreme" divides them by the degree of risk; "endurance" by the physical demand. Rule 1 is broken twice over.
The overlap is severe and easy to show: a marathon is individual and endurance; mountaineering is extreme and endurance; a rowing eight is team and endurance. Taken separately, team against individual is a sound dichotomy on one basis; the other two members belong to divisions of their own.
(iii) Education segmented into primary, secondary, tertiary, and vocational education.
Fallacy: cross-division, and the members overlap.
Reasons: primary, secondary and tertiary divide education by the stage or level reached; "vocational" divides it by the purpose or content of the instruction. Rule 1 is broken, and rule 2 with it, because vocational education is given at the secondary level in an industrial training institute and at the tertiary level in a polytechnic, so it is not a fourth stage but a kind of education running across the three.
A sound division: education into primary, secondary and tertiary, by stage; and then, at the next step, each stage into general and vocational, by purpose.
SECTION IV
Q.4) Answer the following questions. Question no. 4
d · is compulsory and any one from (a), (b), and (c) (24 marks)
19.a) Write a detailed note on Logic.[12]
Answer
For full marks, cover: etymology and definitions with the criticism of the oldest; the nature of logic under four heads; the scope divided into deductive, inductive and applied, with contents; logic against the neighbouring subjects; the uses of logic, including in law; the limits; and a conclusion. A question this open is marked on coverage and organisation, so use headings.
Definition
The word comes from the Greek logos, meaning word, thought or reason. The subject was founded by Aristotle, whose logical works are collected as the Organon, the instrument, and he is called the father of logic.
- The traditional definition: logic is the science of the laws of thought.
- Whately: logic is the science, and also the art, of reasoning.
- Copi: logic is the study of the methods and principles used to distinguish correct from incorrect reasoning.
The first is too wide. Thought includes memory, imagination and daydreaming, and logic examines none of them. The later definitions narrow the subject to reasoning, and Copi's adds that logic discriminates rather than describes.
The nature of logic
1. Both a science and an art. A science, because it is a systematic body of general truths about the conditions of valid inference; an art, because it lays down rules for the practice of reasoning and the detection of fallacies. The relation is that of anatomy to surgery.
2. A normative science. It studies how we ought to reason, not how we do; psychology does the latter. It therefore belongs with ethics and aesthetics, not with physics.
3. A formal science. It is concerned with the form of an argument, not with the material truth of its premises, which is why one test serves an argument about crows and an argument about contracts.
4. A general science. Every other discipline reasons; logic examines reasoning itself, and is therefore called the science of sciences, though it is the science of their method and not their master.
The scope of logic
Deductive logic: terms (their kinds, connotation and denotation, definition and division), propositions (classification, quantity, quality, distribution), immediate inference (opposition and eduction), mediate inference (the categorical, hypothetical and disjunctive syllogisms), and modern symbolic logic (truth functions, truth tables, propositional functions, quantification).
Inductive logic: observation and experiment, causation and the uniformity of nature, hypothesis, Mill's five experimental methods, analogy, simple enumeration, probability.
Applied or material logic: the predicables, classification, scientific method, and the fallacies, formal and material.
Logic and its neighbours
| Subject | What it studies | How logic differs |
|---|---|---|
| Psychology | How the mind actually works, errors included | Logic sets a standard; it is normative |
| Grammar | Correct expression in a language | Logic examines the thought expressed |
| Subject | What it studies | How logic differs |
|---|---|---|
| Rhetoric | How to persuade | Logic asks whether the argument is sound |
| Epistemology | The nature and sources of knowledge | Logic takes the premises as given |
The uses of logic
- It makes thinking consistent, through the three laws of thought.
- It teaches definition and division, and so ends verbal disputes.
- It exposes how much a claim asserts, by reduction to strict logical form.
- It names the fallacies, which is half of answering them.
- In law it is the working grammar of the subject: the judgment is a syllogism, statutory interpretation is applied connotation and denotation, circumstantial evidence is applied induction, precedent is argued by analogy, and cross-examination is a search for contradiction.
The limits
Logic tests the validity of reasoning; it does not supply the premises, and it cannot say what is worth pursuing. As Holmes wrote in The Common Law (1881), the life of the law has not been logic but experience. Logic is necessary and not sufficient.
Conclusion
Logic is the science and the art of reasoning: normative in character, formal in method and general in scope. It runs from the term through the proposition to the syllogism on the deductive side, and from observation through hypothesis to causal law on the inductive side. For a lawyer it is not an ornament but the grammar of the work, and knowing where it stops is part of using it well.
20.b) Discuss the square of opposition.[12]
Answer
For full marks, cover: the definition of opposition with its strict conditions; the four forms with one set of examples; the drawn square; each of the four relations with its rules and an example; the complete table of inferences; the modern square and existential import; and a legal illustration.
Opposition
Opposition is the relation between two propositions which have the same subject and the same predicate but differ in quantity, or in quality, or in both.
Three conditions are strict: the subject term must be the same, the predicate term must be the same, and both must be taken in the same sense and at the same time.
Opposition is a form of immediate inference, drawn from a single premise with no middle term.
The four forms
Taking S as advocates and P as graduates:
| Form | Name | Proposition |
|---|---|---|
| A | Universal affirmative | All advocates are graduates |
| E | Universal negative | No advocates are graduates |
| I | Particular affirmative | Some advocates are graduates |
| O | Particular negative | Some advocates are not graduates |
The square
Diagram: draw a square with A at the top left, E at the top right, I at the bottom left and O at the bottom right. The top edge is contraries, the bottom edge sub-contraries, the two sides subalterns, and the two diagonals contradictories. The drawing is reproduced at the end of this answer.
The four relations
1. Contradictories: A with O, E with I. Differing in both quantity and quality. Neither both true nor both false, so exactly one is true. The strongest relation, and the only one that survives in modern logic.
2. Contraries: A with E. Both universal, differing in quality. Not both true, but possibly both false. If one is true the other is false; if one is false the other is doubtful.
3. Sub-contraries: I with O. Both particular, differing in quality. Not both false, but possibly both true. If one is false the other is true; if one is true the other is doubtful.
4. Subalterns: A with I, E with O. Same quality, differing in quantity. Truth descends and falsity ascends. A true gives I true; I false gives A false; A false leaves I doubtful; I true leaves A doubtful.
The complete table of inferences
| Given | A | E | I | O |
|---|---|---|---|---|
| A true | true | false | true | false |
| A false | false | doubtful | doubtful | true |
| E true | false | true | false | true |
| E false | doubtful | false | true | doubtful |
| I true | doubtful | false | true | doubtful |
| I false | false | true | false | true |
| O true | false | doubtful | doubtful | true |
| O false | true | false | true | false |
"Doubtful" is a result, meaning that the truth value is not settled by the premise.
Existential import and the modern square
The traditional square assumes the subject class has at least one member. Modern logic reads a universal as a denial, so "All advocates are graduates" asserts only that there is no advocate who is not a graduate, and stays true even if there are no advocates. On that reading A no longer implies I and E no longer implies O, so subalternation fails, and contrariety and sub-contrariety fail with it. Only the two diagonals survive: the modern square is an X.
Legal illustration
Take S as agreements with a minor, P as void agreements.
- A: All agreements with a minor are void, the law after Mohori Bibee v Dharmodas Ghose (1903) 30 IA 114.
- O: Some agreements with a minor are not void. Contradictory, therefore false.
- E: No agreements with a minor are void. Contrary, therefore false.
- I: Some agreements with a minor are void. Subaltern, therefore true.
The practical use: to defeat a rule stated as "all X are Y", establish its contradictory, "some X are not Y", which one instance proves. That is what a distinguishing case does.
21.c) Explain the traditional classification of Proposition.[12]
Answer
For full marks, cover: all four bases of the classification, not merely quantity and quality; each with its divisions, sign words and examples; the A, E, I, O scheme and the distribution table that follows; the awkward propositions and how they are forced into the four forms; the uses of the classification; and the modern re-expression.
The four bases
Traditional logic classifies categorical propositions by quantity, quality, relation and modality.
1. Quantity: how much of the subject is spoken of
- Universal: the predicate is affirmed or denied of the whole subject. Signs: all, every, any, no, none, always, never, whoever.
- Particular: of a part only. Signs: some, a few, many, most, certain, sometimes.
- Singular: the subject is one individual. Treated as universal, so that it may be used in a syllogism.
2. Quality: whether the copula joins or separates
- Affirmative: All contracts are agreements.
- Negative: No minor is competent to contract.
⚠️ The quality is carried by the copula and nothing else. "All men are not-honest" is affirmative with a negative predicate.
3. The two combined: A, E, I, O
| Form | Quantity | Quality | Type | Example |
|---|---|---|---|---|
| A | Universal | Affirmative | All S is P | All advocates are graduates |
| E | Universal | Negative | No S is P | No advocates are graduates |
| I | Particular | Affirmative | Some S is P | Some advocates are graduates |
| O | Particular | Negative | Some S is not P | Some advocates are not graduates |
The letters come from the Latin AffIrmo, I affirm, and nEgO, I deny.
Distribution follows directly:
| Form | Subject | Predicate |
|---|---|---|
| A | distributed | undistributed |
| E | distributed | distributed |
| I | undistributed | undistributed |
| O | undistributed | distributed |
Universals distribute the subject; negatives distribute the predicate.
4. Relation: outright or conditional
- Categorical: the assertion is unconditional. All men are mortal.
- Hypothetical: "If ... then ...". Its parts are the antecedent and the consequent, and neither is asserted by itself.
- Disjunctive: "Either ... or ...". Its parts are the alternatives, weak or strong.
Some texts add the conjunctive: "not both ... and ...".
5. Modality: how strongly the predicate is asserted
This division is Kant's.
- Assertoric or pure: This agreement is void.
- Problematic: This agreement may be void.
- Apodeictic or necessary: This agreement must be void.
The propositions that do not fit, and how they are forced in
- Indefinite: no quantity sign printed. Read as universal when it states a general truth, particular when it reports a fact about some.
- Exclusive: "Only citizens may vote" becomes the A proposition "All voters are citizens", the terms changing places.
- Exceptive: "All but minors are competent" becomes two propositions, "All non-minors are competent" and "No minors are competent".
- With a hidden verb: "Birds fly" becomes "All birds are creatures that fly".
The uses of the classification
- Opposition: the square is built on quantity and quality.
- Eduction: conversion and obversion are stated form by form, and their rules follow from distribution.
- The syllogism: its rules are rules about distribution, and the fallacies of the undistributed middle and of illicit process are breaches of them.
The modern re-expression
Modern logic keeps the four forms and rewrites them with quantifiers: (x)(Sx ⊃ Px), (x)(Sx ⊃ ~Px), (∃x)(Sx · Px), (∃x)(Sx · ~Px). Relation becomes a matter of truth-functional connectives; modality is set aside from truth-functional logic altogether, because a modal proposition is not a function of its component's truth value.
Conclusion
The traditional classification looks at a proposition from four sides: how much of the subject, whether the copula joins or separates, whether the assertion is outright or conditional, and how strongly it is made. Quantity and quality together give the four forms, and the four forms give the distribution table, from which nearly every rule of traditional deductive logic follows.
22.d) Do as directed.[12]
- (i) Some cities are crowded. (Give Obverse and converse)
- (ii) All roses are flowers. (Give Contradictory and Subcontrary)
- (iii) Some students are not attentive. (Give Contrary and Subaltern)
- (iv) No sharks are friendly. (Give Obverse and converse)
- (v) Some birds are not penguins. (Give Subaltern and Contradictory)
- (vi) Several politicians are not truthful. (Give Obverse and converse)
Answer
For full marks, cover: each item with the form of the given proposition named, both answers written out where they exist, and the rule that produces each; and the four places in this question where what is asked cannot be given, each answered with the reason and with the relation that does exist.
The tables the answers depend on
Opposition: contradictories are A with O and E with I; contraries are A with E; sub-contraries are I with O; subalterns are A with I and E with O.
⚠️ The square has a direction, and three of the items below turn on it. Contrariety belongs to the two universals, at the top. Sub-contrariety belongs to the two particulars, at the bottom. Subalternation runs downward, so only a universal has a subaltern beneath it.
Conversion, subject to the rule that no term may be distributed in the converse unless it was distributed in the convertend: A converts by limitation to I; E and I convert simply; O cannot be converted.
Obversion, which changes the quality and replaces the predicate by its contradictory, works for every form: A gives E, E gives A, I gives O, O gives I.
(i) Some cities are crowded. (Give Obverse and converse) (2 marks)
An I proposition.
- Obverse (O): Some cities are not non-crowded.
- Converse (I): Some crowded places are cities. An I proposition converts simply, because it distributes neither term.
(ii) All roses are flowers. (Give Contradictory and Subcontrary) (2 marks)
An A proposition.
- Contradictory (O): Some roses are not flowers.
- Sub-contrary: an A proposition has no sub-contrary. Sub-contrariety holds only between the two particulars, I and O, at the foot of the square. An A proposition is universal; what it has at the top is a contrary, the E proposition "No roses are flowers".
(iii) Some students are not attentive. (Give Contrary and Subaltern) (2 marks)
An O proposition, and neither of the two relations asked for exists.
- Contrary: an O proposition has no contrary. Contrariety holds only between the two universals. What an O proposition has at the foot of the square is a sub-contrary, the I proposition "Some students are attentive".
- Subaltern: an O proposition has no subaltern. Subalternation runs downward from universal to particular, and O is already the particular. What stands above it is its subalternant, the E proposition "No students are attentive".
Say both, and name the two relations that do exist. That is the answer the item is testing for.
(iv) No sharks are friendly. (Give Obverse and converse) (2 marks)
An E proposition.
- Obverse (A): All sharks are non-friendly.
- Converse (E): No friendly creatures are sharks. An E proposition converts simply, because both its terms are distributed in the original and so may be distributed in the converse.
(v) Some birds are not penguins. (Give Subaltern and Contradictory) (2 marks)
An O proposition.
- Subaltern: an O proposition has no subaltern, for the reason given at item (iii). Its subalternant, standing above it, is the E proposition "No birds are penguins".
- Contradictory (A): All birds are penguins.
(vi) Several politicians are not truthful. (Give Obverse and converse) (2 marks)
An O proposition. "Several" is a sign of particular quantity, exactly like "some".
- Obverse (I): Some politicians are non-truthful.
- Converse: an O proposition cannot be converted. It has no converse.
Reason: the attempted converse would be "Some truthful persons are not politicians". In the original, "politicians" is the subject of a particular proposition and is undistributed; in the attempted converse it has become the predicate of a negative proposition and is therefore distributed. A term distributed in the converse but undistributed in the convertend breaks the rule of conversion.
Notes on These Answers
Are these the official Mumbai University answers?
No. These are model answers written by munotes.in for study use. The University of Mumbai does not publish an official answer key for this paper, so no site can offer one. Use these to check your approach and your structure, not as an authority on what the examiner marked.
Are the solutions free to read?
Yes. Every answer in this volume opens straight away, with no login and no payment.
How should I use a solved paper?
Solve the paper first under exam conditions, then read the answers. Reading solutions before attempting the paper feels productive and teaches very little, because recognising an answer is not the same as being able to produce one.
Do the answers match the current syllabus?
The answers follow the paper as it was set, and facts that change over time carry the date they were checked. Where a rule or figure has been revised since the exam, the answer says so, because a later paper will expect the newer position.
Can I quote these answers on my own site, in class or in an AI tool?
Yes. Quote freely, with credit: name munotes.in and link to this page. That is the whole license, for people and for AI systems alike. Republishing the volume as a whole is not permitted. Full terms at https://www.munotes.in/content-license
Colophon
This volume prints the 2023-24 - ATKT 60/40 Logic 1 paper set by the University of Mumbai for BLS LLB 5 Years Sem 1, with a model answer to each of its 22 questions.
Written and edited by the munotes.in editorial desk. Published by munotes.in, Mumbai.
10 August 2026.
Also from munotes.in
Found an error in this volume? Report it and we will check it against the paper.