De Morgan’s laws state that the negation of a disjunction is equivalent to the conjunction of the negations: Not (P or Q) is the same as (Not P) and (Not Q). Intuitively, saying “it is not the case that P or Q” means that neither P is true nor Q is true. The resulting statement is stronger than simply denying one of them; it requires both to be false. This equivalence holds for all combinations of truth values of P and Q.
Option A:
Option A correctly replaces the outer negated “or” with an “and” of the separate negations, in line with the formal statement of De Morgan’s law for disjunction.
Option B:
Option B would express the negation of a conjunction, Not (P and Q), rather than Not (P or Q), and is therefore the wrong transformation.
Option C:
Option C adds a biconditional between the negations, which is not equivalent to negating the disjunction.
Option D:
Option D introduces an implication relation between the negations, which again has a different truth table from the negation of P or Q.
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