If $p, q, r$ are simple propositions with truth values $T, F, T$, then the truth value of $(\sim p \vee q)\; \wedge \sim r \Rightarrow p$ is

If $p, q, r$ are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true then

Which of the following is a contradiction

If $q$ is false and $p\, \wedge \,q\, \leftrightarrow \,r$ is true, then which one of the following statements is a tautology?

$(\sim (\sim p)) \wedge q$ is equal to .........

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?