Identify the quantifier in the following statement and write the negation of the statement.
For every real number $x, x$ is less than $x+1.$

Let $p, q$ and $r$ be the statements:
$p$: $X$ is an equilateral triangle
$q$: $X$ is an isosceles triangle
$r: q \vee \sim p$
Then the equivalent statement of $r$ is:

Rewrite the following statement in the form "$p$ if and only if $q$":
$r:$ If a quadrilateral is equiangular,then it is a rectangle and if a quadrilateral is a rectangle,then it is equiangular.

If $p$: switch $s_1$ is closed,$q$: switch $s_2$ is closed,then the correct interpretation of the following circuit is:

The negation of $\sim s \vee (\sim r \wedge s)$ is equivalent to :

Let $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to