KCET · Maths · Sets and Relations
\( \sim[(-p) \wedge q] \) is logically equivalent to
- A \( p \vee(\sim q) \)
- B \( p \wedge(\sim q) \)
- C \( \sim[p \wedge(\sim q)] \)
- D \( \sim(p \vee q) \)
Answer & Solution
Correct Answer
(A) \( p \vee(\sim q) \)
Step-by-step Solution
Detailed explanation
Given that, \(\sim[(-p) \wedge q]\)
From de-Mougan's Law, we have
\(\sim(p \wedge q)=\sim p \vee \sim q\)
Now
\(-[(\sim p) \wedge q]=\sim(\sim p) \vee \sim q=p \vee(\sim q)\)
From de-Mougan's Law, we have
\(\sim(p \wedge q)=\sim p \vee \sim q\)
Now
\(-[(\sim p) \wedge q]=\sim(\sim p) \vee \sim q=p \vee(\sim q)\)
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