Which one of the following Boolean expressions is a tautology?
$\left( {p \vee q} \right) \wedge \left( {p \vee \sim q} \right)$
$\left( {p \wedge q} \right) \vee \left( {p \wedge \sim q} \right)$
$\left( {p \vee q} \right) \wedge \left( { \sim p \vee \sim q} \right)$
$\left( {p \vee q} \right) \vee \left( {p \vee \sim q} \right)$
If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow( q *(\sim p ))$ is a tautology, then the Boolean expression $p *(\sim q )$ is equivalent to
If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is
Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is
The number of values of $r \in\{p, q, \sim p , \sim q \}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is:
Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively