Q.1 (i) The inverse of statement pattern \((p \vee q) \to (p \wedge q)\) is _____
A. \((p \wedge q) \to (p \vee q)\)
B. \(\sim (p \vee q) \to (p \wedge q)\)
C. \((\sim p \wedge \sim q) \to (\sim p \vee \sim q)\)
D. \((\sim p \vee \sim q) \to (\sim p \wedge \sim q)\)
Best answer
Answer: C. \((\sim p \wedge \sim q) \to (\sim p \vee \sim q)\)
Answer: (c) \((\sim p \wedge \sim q) \to (\sim p \vee \sim q)\)
The inverse of \(A \to B\) is \(\sim A \to \sim B\). Here it is \(\sim (p \vee q) \to \sim (p \wedge q)\). By De Morgan's laws \(\sim (p \vee q) \equiv \sim p \wedge \sim q\) and \(\sim (p \wedge q) \equiv \sim p \vee \sim q\), so the inverse is \((\sim p \wedge \sim q) \to (\sim p \vee \sim q)\).
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