The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to
$3^2 = 10$ and $I$ do not get second prize
$3^2 = 10$ or $I$ do not get second prize
${3^2} \ne 10$ or $I$ get second prize
None of these
The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ is equivalent to
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
$\sim p \wedge q$ is logically equivalent to
Which of the following is a tautology?
If $p : 5$ is not greater than $2$ and $q$ : Jaipur is capital of Rajasthan, are two statements. Then negation of statement $p \Rightarrow q$ is the statement