Question:
The Boolean expression \(\sim(p \vee q) \vee (\sim p \wedge q)\) is equivalent to:
The Boolean expression \(\sim(p \vee q) \vee (\sim p \wedge q)\) is equivalent to:
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Factor common literals in Boolean expressions.
Updated On: Mar 23, 2026
- \(p\)
- \(q\)
- \(\sim q\)
- ~ p
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The Correct Option is D
Solution and Explanation
Step 1: Use De Morgan's law:
\[ \sim (p \vee q) = \sim p \wedge \sim q \]
Step 2: Simplify:
\[ (\sim p \wedge \sim q) \vee (\sim p \wedge q) = \sim p \]
\[ \sim (p \vee q) = \sim p \wedge \sim q \]
Step 2: Simplify:
\[ (\sim p \wedge \sim q) \vee (\sim p \wedge q) = \sim p \]
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