UGC NET Questions (Paper – 1)

Conjunction is the compound statement formed by connecting two propositions with "and". According to its truth table, a conjunction is true only when each conjunct is true. This aligns with our intuitive understanding that both conditions must be met. Therefore the connective described in the question is correctly termed conjunction.

Option A:
Option A is correct because conjunction specifically denotes the logical operator that joins statements with "and" and demands the truth of all of them. It is one of the fundamental truth-functional connectives in propositional logic. The stem’s description matches this behaviour exactly.

Option B:
Option B, disjunction, connects statements with "or" and is usually interpreted in logic as true if at least one of the disjuncts is true. It does not require both components to be true, so it does not fit the question.

Option C:
Option C, implication, represents a conditional statement of the form "if p, then q". Its truth conditions differ significantly from those of conjunction and do not match the requirement that both parts be true.

Option D:
Option D, negation, operates on a single proposition by reversing its truth value. It does not combine two statements at all and thus cannot be the connective described.

Conjunction is the compound statement formed by joining two propositions with “and”. It is defined to be true only when each of its component propositions is true. This truth-functional behaviour is central to classical propositional logic. Therefore the connective described in the stem is correctly called conjunction.

Option A:
Option A, disjunction, is formed using “or” and is usually true when at least one of its components is true. It does not require both components to be true simultaneously. Hence disjunction does not match the condition specified in the question.

Option B:
Option B correctly identifies conjunction as the connective that yields truth only when both conjuncts are true. This exclusive requirement distinguishes it from other connectives. Thus conjunction is the most appropriate answer here.

Option C:
Option C, implication, represents a conditional of the form “if p, then q”. Its truth conditions do not restrict both parts to be true. Therefore implication is not the connective being described.

Option D:
Option D, negation, simply reverses the truth value of a single proposition. It does not join two propositions and so fails to fit the description given in the stem.

Statement B gives the correct falsity condition for inclusive disjunction: it fails only when both components are false. C and D are De Morgan’s laws for negation of conjunction and disjunction, both of which are valid equivalences in classical logic. A is false; a conjunction requires both p and q to be true, not just at least one. E is false because in two-valued logic, a statement and its negation cannot be true together. Therefore B, C and D only are correct.

Option A:
Option A is incomplete as it omits D and so does not state the second De Morgan equivalence, leaving the treatment of negation of disjunction unfinished.

Option B:
Option B is incorrect because it includes E, which claims that a statement and its negation can both be true, contradicting the law of non-contradiction in classical logic.

Option C:
Option C is wrong since it accepts A, which incorrectly describes the truth condition for conjunction, and therefore introduces a clear error into the combination.

Option D:
Option D is correct as it gathers the proper truth condition for disjunction and both De Morgan laws, while excluding A and E, which misrepresent conjunction and the mutual exclusivity of a statement and its negation.

Statements A and B give the standard truth conditions for conjunction and inclusive disjunction. Statement D is correct because p → q is equivalent to ¬p ∨ q in classical logic. Statement E is also true since connectives allow us to build complex propositions from atomic ones. Statement C is false because ¬p is true when p is false, not when p is true. Thus A, B, D and E only form the correct set.

Option A:
Option A is incomplete as it omits E and therefore does not mention the important role of connectives in constructing compound statements, even though A, B and D are true.

Option B:
Option B is correct since it includes all true statements and excludes C, which reverses the meaning of negation. It matches the truth-table definitions that NET candidates must know.

Option C:
Option C is incorrect because it contains C, the wrong description of negation, despite including some true statements, so the overall set cannot be accepted.

Option D:
Option D is also wrong as it retains C and omits A, losing the clear definition of conjunction while endorsing an incorrect statement about negation.

In propositional logic, the connective “and” corresponds to conjunction. A conjunction p and q is true only when both component statements p and q are true simultaneously. Here p says the number is even and q says it is divisible by 3. Putting them together with “and” requires both properties to hold. Thus, the combined statement means that the number must be even and divisible by 3.

Option A:
Option A uses “or” instead of “and,” which corresponds to a different connective (disjunction). It allows numbers that are only even or only divisible by 3, and hence does not capture the meaning of “p and q.”

Option B:
Option B mixes “either” with a negation in a way that is not equivalent to the original conjunction. It introduces “not divisible by 3,” which is not part of q.

Option C:
Option C reflects the standard interpretation of a logical conjunction: both conditions must be simultaneously satisfied. It directly translates “p and q” into ordinary language as “even and divisible by 3.”

Option D:
Option D makes both properties false, which would correspond to the negation of p and q, not the conjunction of p and q.