Which of the following pairs are not logically equivalent ?
$ \sim \left( { \sim p} \right)$ and $p$
$p\, \vee \,\left( {p\, \wedge \,q} \right)$ and $q$
$ \sim \,\left( {p\, \wedge \,q} \right)$ and $\left( { \sim p} \right)\, \vee \,\left( { \sim q} \right)$
$ \sim \left( { \sim p\, \wedge \,q} \right)$ and $\left( {p\, \vee \, \sim \,q} \right)$
If the truth value of the statement $p \to \left( { \sim q \vee r} \right)$ is false $(F)$, then the truth values of the statement $p, q, r$ are respectively
Consider the following statements
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as
Which of the following is true
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 following two propositions:
$P_1: \sim( p \rightarrow \sim q )$
$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$
If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then