Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is
There exist a real number $x$ such that neither $x \geq 5\,$ nor $x \leq 5\,$
For every real number, either $x < 5$ or $x > 5$
There exist a real number $x$ such that neither $x > 5$ nor $x < 5$
None of these
The logically equivalent of $p \Leftrightarrow q$ is :-
Which of the following is not a statement
Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is
The maximum number of compound propositions, out of $p \vee r \vee s , p \vee P \vee \sim s , p \vee \sim q \vee s$,
$\sim p \vee \sim r \vee s , \sim p \vee \sim r \vee \sim s , \sim p \vee q \vee \sim s$, $q \vee r \vee \sim s , q \vee \sim r \vee \sim s , \sim p \vee \sim q \vee \sim s$
that can be made simultaneously true by an assignment of the truth values to $p , q , r$ and $s$, is equal to
The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to