Question:
The Boolean expression:
\[
\neg (p \vee q) \vee (\neg p \wedge q)
\]
is equivalent to:
The Boolean expression:
\[
\neg (p \vee q) \vee (\neg p \wedge q)
\]
is equivalent to:
Show Hint
Using De Morgan's law and distribution simplifies complex Boolean expressions.
Updated On: Mar 26, 2025
- \( p \)
- \( q \)
- \( \neg q \)
- \( \neg p \)
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The Correct Option is D
Solution and Explanation
Applying De Morgan's Law:
\[
\neg (p \vee q) = \neg p \wedge \neg q
\]
Thus:
\[
(\neg p \wedge \neg q) \vee (\neg p \wedge q)
\]
Using distributive law:
\[
\neg p \wedge (\neg q \vee q)
\]
Since \( \neg q \vee q = 1 \) (tautology):
\[
\neg p \wedge 1 = \neg p
\]
Thus, the Boolean expression simplifies to:
\[
\neg p
\]
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