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MHT CET202314 May 2023Morning ShiftMathematicsMathematical ReasoningActual

The statement [( p q ) q ] r is a tautology, when r is equivalent to

Options

  1. Ap q
  2. Bq p
  3. Cp q
  4. Dq

Correct answer

D. q

Step-by-step solution

array |c|c|c|c|c|c|c| p & q & r & p q & q & ( p q ) q & [( p q ) q ] r T & T & T & T & F & F & T T & T & F & T & F & F & T T & F & T & F & T & F & T T & F & F & F & T & F & T F & T & T & T & F & F & T F & T & F & T & F & F & T F & F & T & T & T & T & T F & F & F & T & T & T & F array [(p q) q] r is a tautology when all the entries in the last column are T , which is only possible when r q

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