The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:

Which of the following  statements is $NOT$  logically equivalent to $\left( {p \to  \sim p} \right) \to \left( {p \to q} \right)$?

Consider the following statements:

$P :$ Ramu is intelligent

$Q $: Ramu is rich

$R:$ Ramu is not honest

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as.

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

When does the current flow through the following circuit

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: