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
Which Venn diagram represent the truth of the statement“All students are hard working.”
Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
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$?$
If $p \to ( \sim p\,\, \vee \, \sim q)$ is false, then the truth values of $p$ and $q$ are respectively .
Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.