The Boolean function \([\sim (\sim p \wedge q)\wedge \sim(\sim p \wedge \sim…
2016
The Boolean function \([\sim (\sim p \wedge q)\wedge \sim(\sim p \wedge \sim q)] \vee (p \wedge r)\) is equal to the Boolean function :
- A.
\(q\) - B.
\(p \wedge r\) - C.
\(p \vee q\) - D.
\(p\)
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Correct answer: D
Step 1: Apply De Morgan's laws to the left part.
¬(¬p ∧ q) = p ∨ ¬q and ¬(¬p ∧ ¬q) = p ∨ q.
(p ∨ ¬q) ∧ (p ∨ q) = p ∨ (¬q ∧ q) = p ∨ false = p.
Now include the right part: p ∨ (p ∧ r) = p by the absorption law.
Therefore the entire Boolean function simplifies to p.
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