BLS LLB 5 Years Sem 1 Logic 1 2025-26 - ATKT Set 2 60/40 Question Paper with Solutions

Inference is the mental process by which the mind passes from one or more propositions, called the premises, to another proposition, called the conclusion, which is asserted on the strength of them.

Its three marks are:

1. There must be two or more propositions.
2. There must be a relation of implication, so that the conclusion follows.
3. The conclusion must be asserted because of the premises, not merely after them.

Example: "All men are mortal; Socrates is a man; therefore Socrates is mortal."

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.

The totum divisum is the whole that is being divided: the class, or genus, which a logical division breaks up into its species.

It is one of the three elements of every division:

1. the totum divisum, the whole or genus divided;
2. the membra dividentia, the dividing members, that is, the species produced;
3. the fundamentum divisionis, the single attribute on the basis of which the division is made.

Example: in the division of triangle into equilateral, isosceles and scalene, "triangle" is the totum divisum, the three kinds are the membra dividentia, and the length of the sides is the fundamentum divisionis.

Immediate inference is an inference drawn from a single premise, without the help of a middle term: the conclusion follows directly from one proposition.

Its two branches are:

1. Opposition, where the subject and predicate stay unchanged and only the quantity or the quality differs. From "All advocates are graduates" being true it follows immediately that "Some advocates are not graduates" is false.
2. Eduction, where the terms change place or are replaced by their contradictories: conversion, obversion, contraposition and inversion.

A categorematic word is a word which can stand by itself as a term, that is, which can be used alone as the subject or the predicate of a proposition.

Examples: man, judge, table, honest, mortal.

It is contrasted with:

1. Syncategorematic words, which cannot stand alone as a term but only help to make one: all, some, no, and, or, not, is, of, very.
2. Acategorematic words, which can be neither a term nor part of one: interjections such as alas, oh, hurrah.

The law of inverse variation

As the connotation of a term increases, its denotation decreases, and as the connotation decreases, the denotation increases.

man → Indian man → educated Indian man → educated Indian man practising law

Each step adds an attribute and narrows the class.

Its limits. The law holds only along a single line of subordination, genus to species to sub-species. It does not hold where the attribute added belongs to every member already, since "rational man" adds a word and removes nobody, and it does not hold between two terms not related as genus and species.

Terms that have only one of the two

1. Proper names (Rama, the Ganga) denote an individual but, on the traditional view, connote nothing, because they identify without describing.
2. Abstract terms (whiteness, justice, honesty) connote a quality but denote no class of individuals.
3. General terms have both, and are what logic ordinarily works with.

For full marks, cover: all three laws with their statement and symbolic form; an example of each; why they are called laws of thought; their use in argument and in law; and the standard criticisms.

The three laws

1. The Law of Identity. Whatever is, is. Everything is identical with itself, and a term must keep the same meaning throughout an argument.

A is A, or p ⊃ p

Example: "A contract is a contract." Its practical force is that "bank" must mean the same thing in the premise and in the conclusion.

2. The Law of Contradiction. Nothing can both be and not be at the same time and in the same respect. Two contradictory propositions cannot both be true.

~(p · ~p)

Example: "This agreement is void" and "This agreement is not void" cannot both be true of the same agreement at the same time.

2. Contradiction is what makes reductio ad absurdum work: derive a contradiction from an assumption and the assumption is refuted.
3. Excluded middle is what licenses proof by elimination: rule out every alternative but one and the one that remains is established.

In law all three are enforced daily. A statute is presumed to use the same word in the same sense throughout, which is Identity. A written statement that admits and denies the same fact is bad, which is Contradiction. And the circumstantial-evidence rule that the chain must exclude every hypothesis except guilt is Excluded Middle put to work.

Criticisms

1. They are formal and empty. They tell us nothing about the world, and no new knowledge follows from them.
2. Change escapes them. Hegel and the dialectical school argued that a thing in the process of becoming both is and is not what it is turning into.
3. Modern many-valued logics abandon Excluded Middle, admitting a third value for propositions that are neither true nor false.

For full marks, cover: what each word applies to; the definitions; the six combinations with an example of each; the one combination that cannot occur; soundness; and the legal application.

The distinction

Truth and falsity are properties of propositions. Validity and invalidity are properties of arguments. To call a proposition valid, or an argument true, is a category mistake.

• A proposition is true when it corresponds to fact, and false when it does not.
• An argument is valid when the conclusion follows necessarily from the premises, that is, when it is impossible for the premises to be true and the conclusion false.

Validity therefore depends on the form of the argument, not on the material truth of what is asserted, which is why logic is called a formal science.

The six combinations

Soundness

An argument is sound when it is valid and all its premises are true. Only a sound argument guarantees a true conclusion; validity alone guarantees only that no truth has been lost on the way.

It is a crime, punishable under Section 290 IPC (Section 292 BNS). Instances: obstructing a public highway, fouling a public water source, carrying on a noxious trade in a crowded locality.

An individual may sue in tort only on proof of special damage, that is, damage over and above that suffered by the public at large (Campbell v Paddington Corporation [1911] 1 KB 869). Otherwise the remedies are public: Section 91 of the Code of Civil Procedure 1908 allows a suit by the Advocate General or by two or more persons with leave of the court, and Section 133 of the Code of Criminal Procedure 1973, now Section 152 of the Bharatiya Nagarik Suraksha Sanhita 2023, gives a magistrate power to make a conditional order for removal.

Private nuisance

An unreasonable interference with a particular person's use or enjoyment of land. Its essentials are an unreasonable interference, with the use or enjoyment of land or a right over it, causing damage.

It is a tort, and only the occupier of the affected land may sue. Instances: noise, smoke, smell, dust, vibration, encroaching branches.

(1) Reduction to logical form, with the distributed terms

A proposition is in strict logical form when it reads

quantity sign + subject term + copula (is or are, present tense) + predicate term

and can be read off at once as A, E, I or O. The distribution rule is:

Reason: "Every" is a universal sign. The finite verb "requires" 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. The predicate is undistributed: the proposition says nothing about every agreement that requires consent.

(2) "Either the accused confesses or the prosecution proves the charge"

Identification: a compound proposition; the connective is disjunction, signalled by "either ... or".

• Let p = The accused confesses.
• Let q = The prosecution proves the charge.

Symbolic form: p v q

The components are called disjuncts. Taken in the weak or inclusive sense, which is the sense logic gives the symbol, the proposition asserts that at least one of the two holds and possibly both.

Truth table

The two rules that decide every answer

The universal quantifier takes an implication; the existential quantifier takes a conjunction.

• (x) is the universal quantifier: "for every x".
• (∃x) is the existential quantifier: "there is at least one x such that".

(i) Every lawyer respects justice. (Lx, Rx)

(x)(Lx ⊃ Rx)

Read: for every x, if x is a lawyer, then x respects justice. This is an A proposition, universal affirmative.

(ii) Some judges are impartial. (Jx, Ix)

(∃x)(Jx · Ix)

The rules a definition must satisfy

1. It must state the essential attributes, per genus et differentiam.
2. It must not be circular.
3. It must be co-extensive with the term defined, neither too wide nor too narrow.
4. It must not be in obscure or figurative language.
5. It must not be negative where it can be affirmative.

Note the words "if any" in the question. Two of the three items below are sound.

(i) In French, 'tabla' means table.

Identification: a biverbal definition, that is, a definition by synonym in another language. No fallacy.

Reasons: freedom in any legal or moral sense is not a right to do anything whatever. The definition takes in assault, theft and defamation, none of which any system of freedom protects, so it covers far more than the term defined and fails the test of convertibility in one direction. What it defines is licence, not liberty. The differentia is missing, namely the limit that one person's freedom ends where another's rights begin. A sound definition names it: freedom is the condition of being able to act as one chooses, so far as the equal rights of others and the law allow.

Its legal counterpart: Article 19(1) of the Constitution confers freedoms and Articles 19(2) to 19(6) at once state the reasonable restrictions, which is the differentia written into the text.

(iii) A bachelor is an unmarried adult man.

No fallacy. This is a correct definition per genus et differentiam.

Reasons: the proximate genus is "adult man" and the differentia is "unmarried". It is exactly co-extensive: every bachelor is an unmarried adult man and every unmarried adult man is a bachelor, so it converts in both directions. It is not circular, not obscure and not too wide or too narrow.

The rules of logical division

1. Only one fundamentum divisionis at each step; breach is cross-division.
2. The members must be mutually exclusive; breach is overlapping division.
3. The division must be exhaustive; breach is incomplete division.
4. It must proceed step by step; breach is the saltus in dividendo.
5. Every member must be a species of the genus divided.

Again, note "if any". One of the three below is sound.

(i) Car into white, black, big, small.

Fallacy: cross-division, and the members are not mutually exclusive.

(iii) Numbers into odd and even.

No fallacy. This is a sound division, and a dichotomy in effect.

Reasons: one fundamentum divisionis is used, divisibility by two. The members are mutually exclusive, since no whole number is both odd and even, and exhaustive, since every whole number is one or the other. Every rule is satisfied.

The one qualification worth adding: the division is exhaustive of the integers, which is plainly the sense in which "numbers" is meant here. If "numbers" were taken to include fractions and irrationals, neither odd nor even would apply to them and the division would fail rule 3. Stating the universe of discourse is part of stating the division.

For full marks, cover: a definition to open with; the nature of logic under four heads; the scope divided into deductive, inductive and applied; the utility split deliberately into legal education and court argumentation, which is what this question asks and the ordinary "utility in law" question does not; the limits; and a conclusion.

Definition, briefly

Logic is the science and the art of reasoning: the study of the methods and principles by which correct reasoning is distinguished from incorrect. The word is from the Greek logos, and the subject was founded by Aristotle, whose logical works are the Organon.

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. Anatomy and surgery stand in the same relation.

Applied or material logic: definition, division and classification, the predicables, scientific method, and the fallacies, formal and material.

Practical utility in legal education

1. It teaches the student to read a statute. Definition clauses fix connotation; the student who knows connotation from denotation can see at once what an Act covers and what it leaves out, and why ejusdem generis is a rule about genus and species.

2. It teaches case reading. Extracting a ratio decidendi means separating the material facts from the accidental, which is the distinction between essence and accident that the predicables set out.

3. It teaches drafting. A definition clause must be neither too wide nor too narrow and never circular; a schedule of categories must use one basis of division or its entries will overlap. The rules of definition and division are drafting rules before they are examination topics.

4. It disciplines legal writing. An answer, an opinion and a judgment are all arguments, and the student who has learned to set out premises and conclusion writes in a form a reader can follow and check.

3. Circumstantial evidence is applied induction. The conditions laid down in Sharad Birdhichand Sarda v State of Maharashtra AIR 1984 SC 1622 require the chain to be complete and to exclude every hypothesis but guilt, which is Mill's method of elimination in judicial dress.

4. Precedent is argued by analogy. To follow a case is to argue relevant resemblance; to distinguish it is to deny that the resemblance is the one that mattered.

5. Fallacies are met daily and naming them answers them. An argument that attacks the person (ad hominem), appeals to pity (ad misericordiam), assumes what it must prove (petitio principii) or proves something other than the point in issue (ignoratio elenchi) is refuted by being named.

6. Cross-examination is a search for inconsistency, that is, for two propositions from one witness that cannot both be true. The Law of Contradiction is the whole theory of it.

For full marks, cover: what a proposition is; each of the four bases of classification in turn with its divisions and examples; the combined A, E, I, O scheme with the distribution table; the treatment of singular propositions; how the traditional scheme compares with the modern one; and a conclusion.

The 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 a subject, a predicate and a copula. Traditional logic classifies propositions on four bases: quantity, quality, relation and modality.

1. Classification according to QUANTITY

Quantity is settled by how much of the subject the proposition is about.

1. Universal: the predicate is affirmed or denied of the whole of the subject. Sign words: all, every, no, none, any.

The quality is carried by the copula and by nothing else. "All men are not-honest" is affirmative with a negative predicate; "All men are not honest" is a different proposition.

3. Quantity and quality combined: A, E, I, O

The letters come from the Latin AffIrmo, I affirm, and nEgO, I deny.

4. Classification according to RELATION

Relation is settled by how the predicate is related to the subject, that is, whether the assertion is made outright or under a condition.

1. Categorical: the assertion is unconditional.

Example: This agreement is void.

1. Problematic: the predicate is asserted as possible. Sign words: may, might, possibly.

Example: This agreement may be void.

1. Apodeictic or necessary: the predicate is asserted as necessary. Sign words: must, necessarily, cannot but.

Example: This agreement must be void.

How the traditional scheme stands today

Modern logic keeps quantity and quality, recasts them as quantifiers, and treats relation as a matter of truth-functional connectives: the hypothetical becomes the conditional p ⊃ q, the disjunctive becomes p v q. Modality it sets aside from truth-functional logic altogether, because a modal proposition is not a function of the truth value of its component: knowing that "this agreement is void" is false does not tell us whether it might have been void. Modal logic is a separate branch built for exactly that reason.

For full marks, cover: the definition of opposition and its strict conditions; the four forms with one set of examples used throughout; the drawn square; the four relations with their rules and examples; the full table of inferences from truth and from falsity; opposition of singular propositions; the modern square and existential import; and a legal illustration.

Definition

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, because the conclusion comes from one premise with no middle term.

The four forms

Taking S as advocates and P as graduates:

2. Contraries: A with E. Both universal, differing in quality. They cannot both be true, but they may both be false.

• If one is true the other is false. If one is false the other is doubtful.
• Both fail together when the class is mixed: "All students are honest" and "No students are honest".

3. Sub-contraries: I with O. Both particular, differing in quality. They cannot both be false, but they may both be 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. The universal is the subalternant, the particular the subalternate. Truth descends and falsity ascends.

• A true, so I true. I false, so A false. A false, so I doubtful. I true, so A doubtful.

The complete table of inferences

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 if there are no advocates at all. 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. Its contradictory, and therefore false.
• E: No agreements with a minor are void. Contrary to A, and false.
• I: Some agreements with a minor are void. Subaltern of A, and true.

Obversion, which changes the quality and replaces the predicate by its contradictory, and which works for all four forms:

(i) All judges are officers of the court. (State Obverse)

An A proposition.

Obverse (E): No judges are non-officers of the court.

(iii) No illegal act is moral. (State Contradictory)

An E proposition.

Contradictory (I): Some illegal acts are moral.

The contradictory differs in both quantity and quality, so the universal negative is answered by the particular affirmative. The two cannot both be true and cannot both be false: if the original is true, this is false.

(iv) Some citizens are taxpayers. (State Sub-contrary)

An I proposition.

Sub-contrary (O): Some citizens are not taxpayers.

Sub-contraries are the two particulars, differing in quality. They cannot both be false, but they may well both be true, and in a mixed class such as this one they are.

(v) All minors are not competent to contract. (State Contrapositive)

Read in its plain legal sense this is an E proposition: "No minors are persons competent to contract." That is the law itself, Section 11 of the Indian Contract Act 1872 as settled in Mohori Bibee v Dharmodas Ghose.

Contraposition is obversion followed by conversion; the full contrapositive adds a second obversion.

The results for the four forms are: A gives the inverse "Some non-S is not P"; E gives "Some non-S is P"; I and O have no inverse at all, because neither can begin the chain.