Identify the type of "Or" used in the following statement and check whether the statement is true or false:
$\sqrt{2}$ is a rational number or an irrational number.

The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
Two lines intersect at a point or are parallel.

Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If a rectangle is a square,then all its four sides are equal.
$q:$ If all the four sides of a rectangle are equal,then the rectangle is a square.

Consider the three statements -
$p: \forall n \in N, 10n-3$ is a prime number,when $n$ is not divisible by $3$.
$q: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.
$r: \sin x$ is an increasing function in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
Then which of the following statement patterns has a truth value of true?

$(\sim (\sim p)) \wedge q$ is equal to .........