The contrapositive of $(p \vee q) \Rightarrow r$ is
$r \Rightarrow (p \vee q)$
$\sim r \Rightarrow (p \vee q)$
$\sim r \Rightarrow \;\sim p\; \wedge \sim q$
$p \Rightarrow (q \vee r)$
Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ and $S _{2}: p \rightarrow( q \vee r )$ Then, which of the following is NOT true$?$
Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is
If $(p \wedge \sim q) \wedge r \to \sim r$ is $F$ then truth value of $'r'$ is :-
$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.