MHT CET · Maths · Mathematical Reasoning
The statement pattern \(\sim(\mathrm{p} \vee \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q})\) is equivalent to
- A \(\sim \mathrm{p}\)
- B \(\mathrm{p}\)
- C \(\sim q\)
- D \(\mathrm{q}\)
Answer & Solution
Correct Answer
(A) \(\sim \mathrm{p}\)
Step-by-step Solution
Detailed explanation
\(\sim(p \vee q) \vee(\sim p \wedge q)\)
\(=(\sim p \wedge \sim q) \vee(\sim p \wedge q)\)
\(\equiv \sim p \wedge(\sim q \vee q)\)
\(\equiv \sim p \wedge T \cong \sim p\)
\(=(\sim p \wedge \sim q) \vee(\sim p \wedge q)\)
\(\equiv \sim p \wedge(\sim q \vee q)\)
\(\equiv \sim p \wedge T \cong \sim p\)
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