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MHT CET · Maths · Mathematical Reasoning

The statement pattern \(\sim(\mathrm{p} \vee \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q})\) is equivalent to

  1. A \(\sim \mathrm{p}\)
  2. B \(\mathrm{p}\)
  3. C \(\sim q\)
  4. D \(\mathrm{q}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sim \mathrm{p}\)

Step-by-step Solution

Detailed explanation

\(\sim(p \vee q) \vee(\sim p \wedge q)\)
\(=(\sim p \wedge \sim q) \vee(\sim p \wedge q)\)
\(\equiv \sim p \wedge(\sim q \vee q)\)
\(\equiv \sim p \wedge T \cong \sim p\)