Question:

The Boolean expression \(\sim(p \Rightarrow (\sim q))\) is equivalent to :

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Use \(p \Rightarrow r \equiv \sim p \vee r\) and De Morgan's law.
Updated On: Nov 11, 2026
  • \(p \wedge q\)
  • \(q \Rightarrow \sim p\)
  • \(p \vee q\)
  • \((\sim p) \Rightarrow q\)
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The Correct Option is A

Solution and Explanation

\(p \Rightarrow (\sim q) \equiv (\sim p)\vee(\sim q)\).
\(\sim\left((\sim p)\vee(\sim q)\right) \equiv p \wedge q\) (De Morgan).
So the expression is equivalent to \(p\wedge q\).
Answer: (1) \(p \wedge q\)
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