Question:

The logical statement (p \( \Rightarrow \) q) \( \Lambda \) ( q \( \Rightarrow \) ~p) is equivalent to :

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Rewrite each implication as (not first) OR second, then simplify with the distributive law.
Updated On: Oct 31, 2026
  • q
  • \( \sim \)p
  • p
  • \( \sim \)q
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The Correct Option is B

Solution and Explanation

\(p\Rightarrow q\equiv\sim p\vee q\) and \(q\Rightarrow\sim p\equiv\sim q\vee\sim p\).
So the statement is \((\sim p\vee q)\wedge(\sim p\vee\sim q)\equiv\sim p\vee(q\wedge\sim q)\equiv\sim p\vee F\equiv\sim p\).
Answer: (B) \(\sim p\)
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