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MHT CET202617 April 2026Evening ShiftMathematicsMathematical ReasoningActual

The negation of (p q) ((p r) , q) is equivalent to ...

Options

  1. Ap q
  2. Bp , r
  3. Cq (p r)
  4. Dp , q

Correct answer

A. p q

Step-by-step solution

Let the given statement be S (p q) ((p r) q) . The negation of a conditional statement X Y is X Y . S (p q) ((p r) q) Applying the negation rule again to the second part: S (p q) ((p r) ( q)) S (p q) ((p r) q) Using the associative and idempotent laws ( q q q ): S p q (p r) Using the absorption law, p (p r) p : S (p (p r)) q S p q Answer: p q

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