The Boolean expression $$(p \Rightarrow q) \wedge (q \Rightarrow \sim p)$$ is equivalent to :
JEE · Math · previous-year question
- A.$$ \sim $$ q
- B.q
- C.p
- D.$$ \sim $$ pcorrect
Answer
D. $$ \sim $$ p
Explanation
$$(p \to q) \wedge (q \to \sim p)$$ $$ \equiv ( \sim p \vee q) \wedge ( \sim q \vee \sim p)\{ p \to q \equiv \sim p \vee q\} $$ $$ \equiv ( \sim p \vee q) \wedge ( \sim p \vee q)$$ {commutative property} $$ \equiv \sim p \vee (q \wedge \sim q)$$ {distributive property} $$ \equiv \sim p$$
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