If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are respectively.

Which of the following statement patterns is a contradiction?
$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$
$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_{3} \equiv (p \vee q) \rightarrow \sim p$
$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$

Check the validity of the statement given below by the method specified against it.
$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).

If the statement pattern $(p \wedge q) \rightarrow (r \vee \sim s)$ is false,then the truth values of $p, q, r$ and $s$ are respectively:

If the statements $p, q$ and $r$ are true,false and true statements respectively,then the truth value of the statement pattern $[\sim q \wedge (p \vee \sim q) \wedge \sim r] \vee p$ and the truth value of its dual statement respectively are

The statement pattern $(p \land q) \to (r \lor \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively