JEE Main202227 Jul 2022Evening ShiftMathematicsMathematical ReasoningActual
If the truth value of the statement P ∧ ~ R → ~ R ∧ Q is F , then the truth value of which of the following is F ?
Options
- AP ∨ Q → ~ R
- BR ∨ Q → ~ P
- C~ P ∨ Q → ~ R
- D~ R ∨ Q → ~ P
Correct answer
D. ~ R ∨ Q → ~ P
Step-by-step solution
We know that A → B is false, when A is true and B is false So, for P ∧ ~ R → ~ R ∧ Q to be false, P ∧ ~ R should be true and ~ R ∧ Q is false. i.e P is true, R is false and Q is false. A B A → B T T T T F F F T T F F T Now, for P ∨ Q → ~ R is F → T ≡ T R ∨ Q → ~ P is F → F ≡ T ~ P ∨ Q → ~ R is T → T ≡ T ~ R ∨ Q → ~ P is T → F ≡ F