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GATE 2021 CE (CE1) – Question 6

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Statement: Either P marries Q or X marries Y. Which is its logical negation?

  1. P does not marry Q and X marries Y.
  2. Neither P marries Q nor X marries Y.
  3. X does not marry Y and P marries Q.
  4. P marries Q and X marries Y.

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Show answer and explanation

Correct answer: (B) Neither P marries Q nor X marries Y.

Explanation

Write the statement as $A\lor B$. De Morgan’s law gives $\neg(A\lor B)=\neg A\land\neg B$: both alternatives must be false. This is “neither P marries Q nor X marries Y”, **B**. Merely denying one alternative does not negate the disjunction.