JEE Main202131 Aug 2021Evening ShiftMathematicsMathematical ReasoningActual
Negation of the statement ( p ∨ r ) ⇒ ( q ∨ r ) is :
Options
- A~ p ∧ q ∧ ~ r
- B~ p ∧ q ∧ r
- Cp ∧ ~ q ∧ ~ r
- Dp ∧ q ∧ r
Correct answer
C. p ∧ ~ q ∧ ~ r
Step-by-step solution
The negation of the statement ( p ∨ r ) ⇒ ( q ∨ r ) is given by ~ p ∨ r ⇒ q ∨ r ≡ ~ ~ p ∨ r ∨ q ∨ r ≡ p ∨ r ∧ ~ q ∨ r ≡ p ∨ r ∧ ~ q ∧ ~ r ≡ p ∨ r ∧ ~ r ∧ ~ q ≡ p ∧ ~ r ∨ r ∧ ~ r ∧ ~ q ≡ ( ( p ∧ ~ r ) ∨ ϕ ) ∧ ( ~ q ) ≡ ( p ∧ ~ r ) ∧ ( ~ q ) ≡ p ∧ ~ q ∧ ~ r