BLS LLB 5 Years Sem 1 Logic 1 February 2026 - 60/40 Question Paper with Solutions

A term is a word or group of words that can stand as the subject or the predicate of a proposition.

A positive term connotes the presence of a quality or attribute. Examples: man, honest, brave, legal, competent.

A negative term connotes the absence of that quality, and is usually formed by prefixing not, non, un, in, dis, or a like particle to the positive term. Examples: not-man, dishonest, non-Indian, illegal, incompetent.

The two are contradictory to each other: between them they exhaust the universe of discourse, so everything is either a man or a not-man.

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.

There are four kinds:

The four are set out in the square of opposition, and the use of the doctrine is that from the truth or falsity of any one of the four forms we can infer the truth, falsity or doubtfulness of the other three. Opposition is therefore a kind of immediate inference, an inference drawn from a single premise.

Section 13 of the Indian Contract Act 1872: "Two or more persons are said to consent when they agree upon the same thing in the same sense." This identity of mind is called consensus ad idem.

Section 14 adds that consent is free when it is not caused by

1. coercion (Section 15),
2. undue influence (Section 16),
3. fraud (Section 17),
4. misrepresentation (Section 18), or
5. mistake (Sections 20, 21 and 22).

Section 10 makes free consent one of the essentials of a valid contract. Where consent is caused by coercion, undue influence, fraud or misrepresentation the agreement is voidable at the option of the party whose consent was so caused (Sections 19 and 19A); where both parties are under a mistake of fact essential to the agreement, it is void (Section 20).

Eduction is a form of immediate inference in which, from a given proposition, another proposition is inferred whose subject or predicate (or both) is either a term of the original proposition or its contradictory, the meaning being kept unchanged.

It is called immediate because it is drawn from a single premise, without a middle term.

Its kinds are:

1. Conversion: the subject and predicate change places. "No horses are bipeds" gives "No bipeds are horses".
2. Obversion: the quality is changed and the predicate is replaced by its contradictory. "All men are mortal" gives "No men are non-mortal".
3. Contraposition: obvert, then convert. "All men are mortal" gives "No non-mortals are men".
4. Inversion: an inference whose subject is the contradictory of the original subject. "All men are mortal" gives "Some non-men are not mortal".

Induction by simple enumeration is that form of induction in which a general conclusion is drawn merely from the fact that all the observed instances agree, and no contrary instance has been observed. It infers from "some" to "all" without discovering any causal connection.

Example: "All the crows I have seen are black; therefore all crows are black."

Its features are:

1. The conclusion is only probable, never certain.
2. It rests on uncontradicted experience, not on the law of causation.
3. A single negative instance destroys it: one white crow ends the generalisation.
4. Its probability rises with the number and the variety of the instances observed.

Bacon dismissed the method as childish (inductio per enumerationem simplicem, ubi non reperitur instantia contradictoria, res puerilis est).

For full marks, cover: what each word applies to; the definitions; the six combinations with an example of each; the one combination that is impossible; 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 to make 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 at the same time.

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

The six combinations

The last row is the whole content of the idea of validity. Every other combination can occur.

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 nothing about the world; it only guarantees that no truth has been lost on the way from the premises to the conclusion.

• The differentia is the essential attribute which distinguishes this species from the other species of the same genus.

Examples

The rules it must satisfy

1. It must state the essential attributes, not accidental ones.
2. It must be co-extensive with the term defined, neither too wide nor too narrow.
3. It must not be circular, that is, must not use the term defined, a synonym of it, or its correlative.

For full marks, cover: the meaning of nuisance; each kind with its essentials and authority; the table of differences; the special damage rule; and the remedies.

Meaning

Nuisance is an unlawful interference with a person's use or enjoyment of land, or of some right over or in connection with it. The word comes from the French nuire, to hurt. The genus "nuisance" divides into two species on a single basis, namely who is affected.

Private nuisance

An unreasonable interference with a particular person's use or enjoyment of their land. Its essentials are:

1. an unreasonable interference,
2. with the use or enjoyment of land or some right over it,
3. causing damage to the plaintiff.

It is a tort, and only the occupier of the affected land may sue. Standard instances are noise, smoke, smell, dust, vibration and encroaching tree branches.

An individual can sue in tort for a public nuisance only on proof of special damage, that is, damage over and above what the general public suffers (Campbell v Paddington Corporation [1911] 1 KB 869; Solatu v De Held (1851) 2 Sim NS 133). 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 the leave of the court, and Section 133 of the Code of Criminal Procedure 1973 (Section 152 of the Bharatiya Nagarik Suraksha Sanhita 2023) empowers a magistrate to make a conditional order for removal.

The differences

For full marks, cover: all six rules; the name of the fallacy each rule guards against; and a worked example of the breach of each.

A definition marks off the connotation of a term. The classical rules, and the fallacy each one excludes, are these.

1. A definition must state the essential attributes of the term defined

It must be per genus et differentiam, and the genus must be the proximate one. A definition that states an accident or a mere property fails.

Breach: "Man is a laughing animal." Laughter is a property, not the essence.

2. A definition must not be circular

The term defined must not appear in the definition, whether directly, through a synonym, or through its correlative. The fallacy is circulus in definiendo.

Breach: "A cause is that which produces an effect." Cause and effect are correlatives, so the reader who does not know one does not know the other either.

6. A definition must be brief and precise

No word may be redundant, and none may be omitted.

Breach: "Water is a transparent, tasteless, odourless, colourless liquid which is drunk by human beings and animals and is used for washing." Everything after "liquid" is description, not definition.

What strict logical form means

A proposition is in strict logical form when it is written as

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

and can be read off at once as one of the four forms A, E, I or O. The copula must be the verb "to be" alone, and the predicate must be a term, not a verb or an adjective standing loose.

The rule of distribution is the second half of the answer:

Reason: "Certain" here is a sign of particular quantity, exactly equivalent to "some". The predicate "atheist" is turned into the term "atheists" so that the copula can be the bare verb "are".

(iii) Great men are always philosophical.

Logical form: "All great men are philosophical persons." (A proposition)

Distribution: the subject "great men" is distributed; the predicate "philosophical persons" is undistributed.

Reason: "always" is a universal sign, here of time, and a proposition true at all times of its subject is true of the whole of its subject. The adjective "philosophical" is made into the term "philosophical persons".

The biconditional is the conjunction of two conditionals, "if p then q" and "if q then p", so the same proposition may be written (p ⊃ q) · (q ⊃ p). The truth table is built showing both, so the equivalence can be seen rather than asserted.

Truth table

Reading of the table: the biconditional is true when both components have the same truth value and false when they differ. The last column is neither all T nor all F, so the proposition is contingent, not a tautology and not a contradiction. The identity of the last two columns proves that p ≡ q and (p ⊃ q) · (q ⊃ p) are logically equivalent.

(ii) Symbolise with the help of quantifiers

1. All innocent people are honest. (Ix, Hx)

(i) Necessity is the mother of invention

Fallacy: the definition is expressed in figurative or metaphorical language. It breaks the rule that a definition must be in clear, literal terms, and must be more intelligible than the term defined.

Reasons: "mother" is used metaphorically; necessity does not literally give birth to anything. The sentence also states no genus and no differentia, so it is not a definition at all but an epigram about the relation between two things. And it is not convertible: many inventions arise from curiosity, accident or profit, so even taken as a statement of fact it is too narrow.

(ii) Ignorance is lack of knowledge

Fallacy: the definition is negative, and it is circular by correlatives.

Reasons: the definition names the genus, plane figure, and one attribute, four-sidedness, but that attribute belongs to every quadrilateral. Rectangles, rhombuses, parallelograms and trapeziums all satisfy it, so the definition covers far more than the thing defined and fails the test of convertibility in one direction: every square is a four sided plane figure, but not every four sided plane figure is a square. The differentia has been left out.

Correct definition: a square is a plane figure bounded by four equal straight lines meeting at right angles.

(i) Literature into poetry, novel, short story and drama

Fallacy: the division is incomplete, and it is also a cross-division.

Reasons: it is incomplete because the essay, the biography, history and criticism are all literature and none of them appears among the members, so the species taken together fall short of the genus. It is a cross-division because two bases are used at one step: poetry and drama are species of literature by literary form, while the novel and the short story are subdivisions of prose fiction by length. A single sound division would be literature into poetry, drama and prose, with prose then divided at the next step.

(ii) Furniture into table, chairs cupboards and blackboards

Fallacy: a dividing member is not a species of the genus divided.

Reasons: a blackboard is not furniture; it is a teaching appliance, and it therefore has no place among the species into which furniture is divided. Rule 5 is broken. The division is incomplete as well, since beds, sofas, desks and almirahs are furniture and are not named.

The first is criticised as too wide, because thought includes memory, imagination and daydreaming, none of which logic examines. Whately's and Copi's definitions narrow the subject to reasoning, and Copi's adds the point that logic is not descriptive but discriminating: it separates the correct from the incorrect.

The nature of logic

1. Logic is both a science and an art. It is a science because it is a systematic body of general truths about the conditions of valid inference. It is an art because it lays down rules for the practice of reasoning and for the detection of fallacies. The relation is that of anatomy to surgery: the science states the principles, the art applies them.

2. Logic is a normative science, not a positive one. It studies how we ought to reason, not how we in fact reason. Psychology describes actual mental processes, including the mistaken ones; logic sets a standard against which those processes are judged. Logic is therefore grouped with ethics and aesthetics, which set standards of the good and the beautiful, and not with physics or chemistry.

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

The utility of logic in law

1. The judgment is a syllogism. The rule of law is the major premise, the facts as found are the minor premise, and the order of the court is the conclusion.

Whoever commits theft shall be punished with imprisonment (Section 379 IPC).
The accused has committed theft.
Therefore the accused shall be punished with imprisonment.

Because the form is a syllogism, an appeal can attack either premise, and the distinction between an appeal on law and an appeal on facts is a distinction between attacking the major and attacking the minor.

2. Statutory interpretation is applied connotation and denotation. A definition clause fixes the connotation of a word and the court decides what falls within its denotation. The rule of ejusdem generis, by which general words following an enumeration are read as limited to the same kind, is nothing but a rule about genus and species.

7. Pleadings and issues rest on the rules of consistency. A written statement that admits and denies the same fact violates the law of contradiction, and the framing of issues under Order XIV of the Code of Civil Procedure is an exercise in isolating the propositions actually in dispute.

The limits of logic in law

Logic tests the validity of legal reasoning; it does not supply the premises. The choice of the rule, the finding of the facts, and the weighing of competing values are not logical operations. As Oliver Wendell Holmes wrote in The Common Law (1881), the life of the law has not been logic but experience. Logic is therefore necessary in law and not sufficient: a judgment that is illogical is certainly wrong, but a judgment can be perfectly logical and still unjust.

For full marks, cover: the definition of opposition; the four categorical forms with one set of examples used throughout; the drawn square; each of the four relations with its rules of inference and an example; the complete table of what follows from the truth and from the falsity of each form; the point about existential import; and a legal illustration.

Meaning of 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. It is a variety of immediate inference, because from the truth or falsity of one proposition we pass directly to a conclusion about another without any middle term.

The four categorical forms

Taking the subject term S as advocates and the predicate term P as graduates:

They differ in both quantity and quality. They can neither both be true nor both be false; exactly one of them is true.

• If "All advocates are graduates" (A) is true, then "Some advocates are not graduates" (O) is false.
• If A is false, then O is true.

This is the strongest of the four relations and the only one that survives in modern logic.

2. Contraries: A and E

Both are universal and they differ in quality. They cannot both be true, but they may both be false.

• If "All advocates are graduates" (A) is true, "No advocates are graduates" (E) is false.
• If A is false, E is doubtful: it may be that no advocate is a graduate, or that some are and some are not.

Both are false whenever the class is mixed, which is why "All students are honest" and "No students are honest" can fail together.

3. Sub-contraries: I and O

Both are particular and they differ in quality. They cannot both be false, but they may both be true.

Existential import and the modern square

The traditional square assumes that the subject class has at least one member. On that assumption A implies I, and E implies O. Modern (Boolean) logic does not make that assumption: a universal proposition is read as a denial, so "All advocates are graduates" only asserts that there is no advocate who is not a graduate, and it would remain true if there were no advocates at all.

The consequence is that in the modern square the subaltern, contrary and sub-contrary relations all disappear, and only the two diagonals, the contradictories, remain. A sentence saying so is worth a mark, and it links this question to the modern classification of propositions asked at 4(c).

Legal illustration

Take S as agreements with a minor and P as void agreements.

• A: All agreements with a minor are void. This is the law after Mohori Bibee v Dharmodas Ghose (1903) 30 IA 114.

The aim of the modern classification

Modern logic, developed by Boole, Frege, Peano, Russell and Whitehead, classifies propositions first into simple and compound. The aims are these.

1. To exhibit truth functional structure. A compound proposition is one whose truth value is determined by the truth values of its components together with the connective. Once propositions are classified this way, the truth value of the whole can be computed from the parts.

2. To remove the ambiguity of ordinary language. Symbols have exactly one meaning. The English "or" is ambiguous between the inclusive and the exclusive sense; the symbol v is fixed as inclusive, so nothing turns on how a sentence happens to be phrased.

3. To supply a decision procedure. The truth table is a mechanical test: any argument in the propositional calculus can be tested for validity in a finite number of steps, without insight or ingenuity. Traditional logic had no such procedure.

4. To separate form from content completely. Symbolising with p, q, r leaves nothing of the subject matter behind, so the same test applies to an argument about scholarships and an argument about statutes.

3. Disjunction (p v q), read "p or q"

The components are called disjuncts. Taken in the weak or inclusive sense, "at least one, possibly both". False only when both disjuncts are false.

The strong or exclusive sense, "one but not both", as in "the accused is either guilty or innocent", is written (p v q) · ~(p · q).

4. Implication or conditional (p ⊃ q), read "if p then q"

The first component is the antecedent and the second the consequent. False only when the antecedent is true and the consequent false.

Compounds that are not truth functional

A compound whose truth value is not determined by the truth values of its components is not truth functional and falls outside this classification. Examples: "Rama believes that the earth is flat", "It is necessary that two and two are four", "Rama died because he was poisoned". Knowing that "the earth is flat" is false does not tell us whether Rama believes it, so the compound is not a function of its component's truth value.

Classification of statement forms

By the last column of the truth table, a compound is:

1. Tautologous, true on every row, for example p v ~p, the law of excluded middle.
2. Contradictory, false on every row, for example p · ~p, which the law of contradiction forbids.
3. Contingent, true on some rows and false on others, for example p ⊃ q, and the biconditional set at Q16 of this paper.

Legal illustration

Statutes are written in these connectives, and the difference between them decides cases.

For full marks, cover: each of the six items answered with the form of the given proposition named, the answer written out in full, and the rule stated; plus the two items where the paper asks for something that cannot be given, answered honestly with the reason.

The two tables the answers depend on

Conversion (subject and predicate change places; no term may be distributed in the converse unless it was distributed in the original):

(2) No dishonest person are brave. Give subaltern and contrary. (2 marks)

The given proposition is an E proposition.

• Subaltern (O): Some dishonest persons are not brave.
• Contrary (A): All dishonest persons are brave.

(3) Some men are not wise. Give contradictory and contrary. (2 marks)

The given proposition is an O proposition.

• Contradictory (A): All men are wise.
• Contrary: an O proposition has no contrary. The relation of contrariety holds only between two universal propositions, A and E, which is why they occupy the top of the square. What stands opposite an O proposition at the foot of the square is its sub-contrary, which is the I proposition: Some men are wise.

Write both: name the sub-contrary, and say why there is no contrary. The rule is that two particulars cannot both be false, and that is sub-contrariety, not contrariety.

(4) No horses are biped. Give converse and obverse. (2 marks)

The given proposition is an E proposition.

• Converse: an O proposition cannot be converted. Take the attempted converse, "Some good orators are not politicians". In the original, "politicians" is the subject of a particular proposition and is therefore 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, so the inference is invalid and O has no converse.
• Obverse (I): Some politicians are non-good-orators, that is, some politicians are not-good orators. The quality changes from negative to affirmative and the predicate is replaced by its contradictory.