Question:

The negation of the Boolean expression \(p\vee(\sim p\wedge q)\) is equivalent to :

Show Hint

Note \(p\vee(\sim p\wedge q)\equiv p\vee q\) by distributivity; then apply De Morgan's law.
Updated On: Nov 5, 2026
  • \(p\wedge\sim q\)
  • \(\sim p\vee\sim q\)
  • \(\sim p\wedge q\)
  • \(\sim p\wedge\sim q\)
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The Correct Option is D

Solution and Explanation

\(p\vee(\sim p\wedge q)=(p\vee\sim p)\wedge(p\vee q)=T\wedge(p\vee q)=p\vee q\).
Negation: \(\sim(p\vee q)=\sim p\wedge\sim q\) (De Morgan).
Answer: (4) \(\sim p\wedge\sim q\)
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