The statement pattern $\sim(p \leftrightarrow \sim q)$ is

If $p$ and $q$ are true statements and $r$ and $s$ are false statements,then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(p \vee s) \leftrightarrow(q \wedge r)$ are respectively

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

Negation of the Boolean statement $(p \vee q) \Rightarrow ((\sim r) \vee p)$ is equivalent to

If the truth value of the compound statement $[(p \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively......

The maximum number of compound propositions,out of $p \vee r \vee s$,$p \vee \sim r \vee \sim s$,$p \vee \sim q \vee s$,$\sim p \vee \sim r \vee s$,$\sim p \vee \sim r \vee \sim s$,$\sim p \vee q \vee \sim s$,$q \vee r \vee \sim s$,$q \vee \sim r \vee \sim s$,$\sim p \vee \sim q \vee \sim s$ that can be made simultaneously true by an assignment of the truth values to $p, q, r$ and $s$,is equal to