The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)$ is True, is equal to
$6$
$7$
$5$
$4$
The negation of the Boolean expression $p \vee(\sim p \wedge q )$ is equivalent to
Which Venn diagram represent the truth of the statement“All students are hard working.”
Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.
If $p \to ( \sim p\,\, \vee \, \sim q)$ is false, then the truth values of $p$ and $q$ are respectively .
The contrapositive of the statement "I go to school if it does not rain" is
If statement $(p \rightarrow q) \rightarrow (q \rightarrow r)$ is false, then truth values of statements $p,q,r$ respectively, can be-