Let $p$ and $q$ denote the following statements:
$p$: The sun is shining
$q$: $I$ shall play tennis in the afternoon
The negation of the statement "If the sun is shining then $I$ shall play tennis in the afternoon" is:

Which of the following is false?

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?

Check whether "Or" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
$t:$ You are wet when it rains or you are in a river.

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:

Identify the quantifier in the following statement and write the negation of the statement.
There exists a number which is equal to its square.