Statement: Either P marries Q or X marries Y.

Among the options below, the logical NEGATION of the above statement is:
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Question

Statement: Either P marries Q or X marries Y.

Among the options below, the logical NEGATION of the above statement is:

A. P does not marry Q and X marries Y.
B. Neither P marries Q nor X marries Y.
C. P does not marry Q and X does not marry Y.
D. P marries Q and X marries Y.

Accepted Answer

B. Neither P marries Q nor X marries Y. The given statement uses the inclusive OR (disjunction): A OR B. The logical negation of a disjunction is a conjunction of the individual negations, by De Morgan's law: NOT(A OR B) = (NOT A) AND (NOT B). Here A = 'P marries Q' and B = 'X marries Y', so the negation is 'P does not marry Q AND X does not marry Y', which is the same as 'Neither P marries Q nor X marries Y'.

Statement: Either P marries Q or X marries Y. Among the options below, the logical NEGATION of the above statement is: A. P does not marry Q and X marries Y. B. Neither P marries Q nor X marries Y. C. P does not marry Q and X does not marry Y. D. P marries Q and X marries Y.