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MHT CET202619 April 2026Morning ShiftMathematicsMathematical ReasoningActual

Which of the following logical statements is a tautology?

Options

  1. A[(p q) q] p
  2. B(p q) (p q)
  3. C[(p q) p] q
  4. D[(p q) ( p q)] r

Correct answer

A. [(p q) q] p

Step-by-step solution

Consider the first option: [(p q) q] p Using logical equivalences, we know that p q p q . Substituting this into the premise: (p q) q ( p q) q ( p q) (q q) ( p q) F p q Now, substituting this back into the original statement: ( p q) p ( p q) p (p q) p (p p) q T q T Since the final truth value is always True ( T ), this statement is a tautology. Checking the other options for completeness: (p q) (p q) ( p q) ( p q) F (Contradiction) [(p q) p] q (q p) q p (q q) F (Contradiction) [(p q) ( p q)] r [(p q p) (p q q)] r (

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