JEE Main202229 Jun 2022Evening ShiftMathematicsMathematical ReasoningActual
Negation of the Boolean statement p ∨ q ⇒ ~ r ∨ p is equivalent to:
Options
- Ap ∧ ~ q ∧ r
- B~ p ∧ ~ q ∧ r
- C~ p ∧ q ∧ r
- Dp ∧ q ∧ ~ r
Correct answer
C. ~ p ∧ q ∧ r
Step-by-step solution
Given, p ∨ q ⇒ ~ r ∨ p ≡ ~ p ∨ q ∨ ~ r ∨ p ≡ ~ p ∧ ~ q ∨ p ∨ ~ r ≡ ~ p ∨ p ∧ ~ q ∨ p ∨ ~ r ≡ ~ q ∨ p ∨ ~ r So negation of ~ q ∨ p ∨ ~ r is ~ p ∧ q ∧ r .