The contrapositive of the statement "If you will work, you will earn money" is ..... .

The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements

$(i)$ $p \leftrightarrow  q$ 

$(ii)$ $~ p \leftrightarrow q$

$(iii)$ $~ q \leftrightarrow p$

$(iv)$ $~ p \leftrightarrow ~ q$

The maximum number of compound propositions, out of $p \vee r \vee s , p \vee P \vee \sim s , p \vee \sim q \vee s$,

$\sim p \vee \sim r \vee s , \sim p \vee \sim r \vee \sim s , \sim p \vee q \vee \sim s$, $q \vee r \vee \sim s , q \vee \sim r \vee \sim s , \sim p \vee \sim q \vee \sim s$

that can be made simultaneously true by an assignment of the truth values to $p , q , r$ and $s$, is equal to

The contrapositive of the statement "If it is raining, then I will not come", is