The contrapositive of $\sim q \to p$ is equivalent to

The simplified switching circuit for the following circuit is (Assume the circuit consists of two switches $S_1$ and $S_2$ in parallel, connected in series with a switch $S_3$):

Find the component statements of the following compound statement and check whether they are true or false.
Number $3$ is prime or it is odd.

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

Which of the following is $NOT$ equivalent to $p \rightarrow q$?

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