Which of the following is always true
$(p \Rightarrow q) \equiv \;\sim q \Rightarrow \;\sim p$
$\sim (p \vee q) \equiv \vee \;p\; \vee \sim q$
$\sim (p \Rightarrow q) \equiv p\; \wedge \sim q$
$\sim (p \vee q) \equiv \;\sim p\;\; \wedge \sim q$
If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?
The statment $ \sim \left( {p \leftrightarrow \sim q} \right)$ is
Statement $p$ $\rightarrow$ ~$q$ is false, if
Consider the following statements :
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
Negation of “Ram is in Class $X$ or Rashmi is in Class $XII$” is