The statement pattern $\sim(p \leftrightarrow \sim q)$ is

The negation of the statement "If a number is divisible by $15$,then it is divisible by $5$ and $3$" is:

Consider the following statements:
$(A)$ If $4+3=8$,then $5+3=9$
$(B)$ If $6+4=10$,then the moon is flat
$(C)$ If both $(A)$ and $(B)$ are true,then $5+6=17$
Which of the following statements is correct?

The given circuit is equivalent to:

Which of the following statements is a tautology?

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?