Question

Which of the following statements is a tautology?

• A. $\sim\left(p\, \wedge\, \sim\, q\right) \rightarrow p\, \vee\, q$
• B. $\sim\left(p\, \vee\, \sim\, q\right) \rightarrow\, p\, \wedge q$
• C. $p \vee \left(\sim q\right) \rightarrow p \wedge q$
• D. $\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q$

Answer 1

The Correct Option is D

\(\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q\)
\(\left(\sim p \wedge q\right) \to p \vee q\)
\(\sim\left\{\left(\sim p \wedge q\right)\wedge \left(\sim p \wedge \sim q\right)\right\}\)
\(\sim\left(\sim p \wedge f\right)\)

So, the correct  option is (D): \(\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q\).