List of top Mathematics Questions on validating statements

The negation of the statement “For every real number $x$, $x^2 + 5$ is positive” is:

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

The negation of the statement "For all real numbers x and y, x + y = y + x" is

The negation of the statement: "Getting above 95% marks is necessary condition for Hema to get the admission is good college"

The negation of the statement "72 is divisible by 2 and 3" is

The negation of $p{\land}(q \to \sim r)$ is

If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively

The negation of the compound proposition $p \vee (\sim p \vee q)$ is.