UGC NET Questions (Paper – 1)

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.