JEE Main202226 Jul 2022Morning ShiftMathematicsMathematical ReasoningActual
The statement ~ p ⇔ ~ q ∧ q is:
Options
- Aa tautology
- Ba contradiction
- Cequivalent to p ⇒ q ∧ q
- Dequivalent to p ⇒ q ∧ p
Correct answer
D. equivalent to p ⇒ q ∧ p
Step-by-step solution
~ p ⇔ ~ q ∧ q = p ⇔ q ∧ q Proof: Solving the given ~ p ⇔ ~ q = ~ p → ~ q ∧ ~ q → p = ~ ~ p ∨ ~ q ∧ q ∨ p = ~ ~ p ∧ q ∧ p ∨ q = p ∧ q ∨ ~ p ∨ q             . . . 1 Now, p ⇔ q ≡ p → q ∧ q → p = ~ p ∨ q ∧ ~ q ∨ p = ~ p ∨ q ∧ ~ q ∨ ~ p ∨ q ∧ p = ~ p ∧ ~ q ∨ q ∧ ~ q ∨ ~ p ∧ p ∨