UGC NET Questions (Paper – 1)

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.

Disjunction is the logical operation that forms a compound statement using "or". In its inclusive sense used in standard logic, a disjunction is true when at least one of the disjuncts is true and false only when both are false. This behaviour corresponds exactly to the description in the stem. Hence the connective is called disjunction.

Option A:
Option A, conjunction, links statements with "and" and is true only when both conjuncts are true. Its falsity conditions are therefore quite different and do not match the pattern described. Thus conjunction is not the correct answer.

Option B:
Option B is correct because disjunction accurately characterises the truth conditions stated: it fails only when neither component is true. This makes disjunction the appropriate technical term for the "or" connective in propositional logic.

Option C:
Option C, biconditional, expresses "p if and only if q" and is true when both components share the same truth value. This is more restrictive than the simple "or" relation and does not correspond to the stem.

Option D:
Option D, negation, alters the truth value of a single statement and does not combine two statements with "or". Consequently negation cannot be the intended connective.

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.

An exclusive “or” implies that choosing one option rules out the other. Examination instructions that say you may answer in English or in Hindi usually mean that you must choose exactly one language for your answer sheet. Answering in both languages is typically not allowed. Thus, the “or” is naturally interpreted as exclusive, indicating a choice between alternatives.

Option A:
Option A invokes a testing context where using both options would violate the implicit rule, so the disjunction is best read as “one but not both,” which captures exclusivity.

Option B:
Option B is often inclusive in practice; some exams allow both a pen and a pencil, so the context does not clearly exclude taking both.

Option C:
Option C can also be inclusive, since meetings can sometimes be open to both students and teachers together.

Option D:
Option D explicitly allows “both,” making the “or” inclusive by directly stating that dual use is possible.