Which of the following statements is a tautology?
$((\sim p) \vee q) \Rightarrow p$
$p \Rightarrow((\sim p ) \vee q )$
$((\sim p) \vee q) \Rightarrow q$
$q \Rightarrow((\sim p) \vee q)$
The statement $(p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$ is equivalent to
$\sim p \wedge q$ is logically equivalent to
If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to