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.

Statements A and B correctly state the meanings of universal and existential quantifiers. Statement D gives the standard rule that the negation of a universal statement becomes an existential statement with negated predicate. Statement E is also true since many mathematical theorems and definitions are framed with such quantifiers. Statement C is false because ∀x P(x) and ∃x P(x) usually have very different truth conditions. Hence A, B, D and E only are correct.

Option A:
Option A is incomplete because it omits E and does not explicitly note the role of quantified statements in formulating general laws and existence results.

Option B:
Option B is wrong because it includes C, the incorrect claim that universal and existential forms are equivalent.

Option C:
Option C is incomplete because it omits A (meaning of ∀) and also does not collect the full correct set together.

Option D:
Option D is correct since it gathers all the true statements and rejects C, which conflates different quantifier types.

Statements A and B restate De Morgan’s laws, showing how negation distributes over “and” and “or”, C correctly defines logical equivalence in terms of matching truth values and D is true because De Morgan’s laws explicitly connect conjunction, disjunction and negation. Statement E is false since contradictory statements cannot both be true in any possible situation; one must be false whenever the other is true. Hence, the combination A, B, C and D only is correct.

Option A:
Option A is incomplete because, although it lists three true statements, it omits D and thus does not explicitly say that De Morgan’s laws are the ones relating “and”, “or” and “not”. Without D, the named connection between these operators is not emphasised.

Option B:
Option B is also incomplete because it leaves out A and thereby fails to include the first De Morgan equivalence concerning the negation of “p and q”. That omission makes the description of the laws partial.

Option C:
Option C is correct as it bundles all four true statements, fully describing De Morgan’s laws and logical equivalence, while rejecting E, which mischaracterises contradictions. It aligns with the logical tools used in UGC NET reasoning.

Option D:
Option D is wrong because it includes E, the false statement about contradictions, and omits C, the formal definition of logical equivalence. This combination mixes error with omission.

B, C, D and E are correct; A is false. The negation of “All S are P” is “Some S are not P”, not “No S are P”. B gives the correct negation of “Some S are P”. C and D are De Morgan’s laws. E is true about exam utility.

Option A:
Option A is incomplete because it omits E (which is true and relevant), so it does not include all correct statements.

Option B:
Option B is incorrect because it includes A, which gives the wrong negation of “All S are P”.

Option C:
Option C is correct because it includes all true statements (B, C, D, E) and excludes A (false).

Option D:
Option D is incorrect because it includes A, which is false, so it cannot be the correct set.