De Morgan laws and disjunction – UGC NET Question

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.