The Boolean expression \((p \wedge \sim q) \Rightarrow (q \vee \sim p)\) is equivalent to :
Show Hint
- \(q \Rightarrow p\)
- \(p \Rightarrow q\)
- \(\sim q \Rightarrow p\)
- \(p \Rightarrow \sim q\)
The Correct Option is B
Solution and Explanation
\((p \wedge \sim q) \Rightarrow (q \vee \sim p) \equiv \sim(p \wedge \sim q) \vee (q \vee \sim p)\).
By De Morgan's law, \(\sim(p \wedge \sim q) = \sim p \vee q\).
So the expression is \((\sim p \vee q) \vee (q \vee \sim p) = \sim p \vee q\).
But \(\sim p \vee q \equiv p \Rightarrow q\).
Answer: (2) \(p \Rightarrow q\)
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