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MHT CET202619 April 2026Morning ShiftMathematicsMathematical ReasoningActual

The logical statement (p q) [( p q) (p q)] q is logically equivalent to ...

Options

  1. Ap q
  2. Bp q
  3. Cp q
  4. Dp q

Correct answer

A. p q

Step-by-step solution

Given statement: (p q) [( p q) (p q)] q Consider the part [( p q) (p q)] q Using distributive law: = (( p q) q) ((p q) q) = ( p (q q)) (p ( q q)) = ( p F) (p q) = F (p q) = p q Now, substitute this back into the original statement: = (p q) (p q) Using distributive law: = (p (p q)) (q (p q)) = ((p p) q) (p (q q)) = (p q) (p F) = (p q) F = p q Answer: p q

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