MHT CET · Maths · Mathematical Reasoning
Simplify \((p \vee q) \wedge(p \vee \sim q)\)
- A \(p\)
- B \(T\)
- C \(\bar{F}\)
- D \(q\)
Answer & Solution
Correct Answer
(A) \(p\)
Step-by-step Solution
Detailed explanation
\((p \vee q) \wedge(p \vee \sim q)\)
\(=p \vee(q \wedge \sim q) \quad\) (distributive law) \(=p \vee 0\)
(complement law)
\(=p\)
(0 is indentity for \(\vee\) )
\(=p \vee(q \wedge \sim q) \quad\) (distributive law) \(=p \vee 0\)
(complement law)
\(=p\)
(0 is indentity for \(\vee\) )
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