MHT CET · Maths · Mathematical Reasoning
The logical expression \([p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]\) is equivalent to
- A \(\mathrm{q}\)
- B \(\sim q\)
- C \(\sim \mathrm{p}\)
- D \(\mathrm{p}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{p}\)
Step-by-step Solution
Detailed explanation
\([p \wedge(q \vee r)] \vee[\sim r \wedge \sim \wedge \wedge p]\)
\(\equiv[p \wedge(q \vee r)] \vee[p \wedge(\sim q \wedge \sim r)]\)
\(\underline{\underline{\underline{\alpha}}}[p \wedge(q \vee r)] \vee[p \wedge(\sim(q \vee r))]\)
\(=p \wedge[(q \vee r) \vee(\sim(q \vee r))]\)
\(=p \wedge T=p\)
\(\equiv[p \wedge(q \vee r)] \vee[p \wedge(\sim q \wedge \sim r)]\)
\(\underline{\underline{\underline{\alpha}}}[p \wedge(q \vee r)] \vee[p \wedge(\sim(q \vee r))]\)
\(=p \wedge[(q \vee r) \vee(\sim(q \vee r))]\)
\(=p \wedge T=p\)
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