The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

The logical equivalent of $p \Leftrightarrow q$ is :-

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

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

Given $p$: $A$ man is a judge,$q$: $A$ man is honest. If $S_1$: If a man is a judge,then he is honest; $S_2$: If a man is a judge,then he is not honest; $S_3$: $A$ man is not a judge or he is honest; $S_4$: $A$ man is a judge and he is honest. Then:

Which of the following is an open statement?