JEE Main202125 Jul 2021Morning ShiftMathematicsMathematical ReasoningActual
The Boolean expression ( p ⇒ q ) ∧ ( q ⇒ ~ p ) is equivalent to :
Options
- A~ q
- Bq
- Cp
- D~ p
Correct answer
D. ~ p
Step-by-step solution
( p ⇒ q ) ∧ ( q ⇒ ~ p ) = ( ~ p ∨ q ) ∧ ( ~ q ∨ ~ p ) p ⇒ q = ~ p ∨ q = ( ~ p ∨ q ) ∧ ( ~ p ∨ ~ q ) commutative property = ~ p ∨ ( q ∧ ~ q ) distributive property = ~ p