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 $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively
If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively
Let $p$ and $q$ denote the following statements
$p$ : The sun is shining
$q$ : I shall play tennis in the afternoon
The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is
The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to
Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow(( p \nabla$q) $\nabla r$ ) is a tautology. Then (p $\nabla q ) \Delta r$ is logically equivalent to