MHT CET · Maths · Mathematical Reasoning
The logical statement \(\sim(p \vee q) \vee(\sim p \wedge q)\) is equivalent to
- A \(\mathrm{q}\)
- B \(\sim q\)
- C \(\sim p\)
- D p
Answer & Solution
Correct Answer
(C) \(\sim p\)
Step-by-step Solution
Detailed explanation
\(\sim(\mathrm{p} \vee \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \equiv(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \) \(\text { [De Morgana’s law] } \)
\( \equiv \sim p \wedge(\sim q \vee q) \quad \text { [Distributive law] } \)
\( \equiv \sim p \wedge t \quad[\because \sim q \vee q \equiv t] \)
\( \equiv \sim \mathrm{p}\)
\( \equiv \sim p \wedge(\sim q \vee q) \quad \text { [Distributive law] } \)
\( \equiv \sim p \wedge t \quad[\because \sim q \vee q \equiv t] \)
\( \equiv \sim \mathrm{p}\)
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