Let $p$ and $q$ be two statements. Amongst the following,the statement that is equivalent to $p \to q$ is

The statement $(p$ $\rightarrow q)$ $\rightarrow ((\sim p$ $\rightarrow q)$ $\rightarrow q)$ is

If $p$: switch $s_1$ is closed,$q$: switch $s_2$ is closed,then the correct interpretation of the following circuit is:

Which one of the following is a tautology?

Write the negation of the following statement:
$p:$ For every positive real number $x,$ the number $x-1$ is also positive.

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.