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JEE Main20203 Sep 2020Evening ShiftMathematicsMathematical ReasoningActual

Let p , q , r be three statements such that the truth value of p ∧ q → ~ q ∨ r is F . Then the truth values of p , q , r are respectively :

Options

  1. AT ,   T ,   F
  2. BT ,   T ,   T
  3. CT ,   F ,   T
  4. DF ,   T ,   F

Correct answer

A. T ,   T ,   F

Step-by-step solution

Given that the truth value of p ∧ q → ~ q ∨ r is F . For the above truth value to be possible, p ∧ q should be TRUE and ~ q ∨ r should be FALSE. p ∧ q is TRUE when p   &   q both are TRUE. ~ q ∨ r is FALSE when q is TRUE and r is FALSE. So, the truth values of p ,   q ,   r are T ,   T ,   F respectively.

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