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

Among the statements

$(S1)$: $(p \Rightarrow q) \vee((\sim p) \wedge q)$ is a tautology

$(S2)$: $(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$ is a contradiction

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

If $q$ is false and $p\, \wedge \,q\, \leftrightarrow \,r$ is true, then which one of the following statements is a tautology?

If $A$ : Lotuses are Pink and $B$ : The Earth is a planet. Then the
verbal translation of $\left( { \sim A} \right) \vee B$ is

Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is