Which of the following logical equivalences is always true?

The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to which of the following?

If the statement pattern $(p \wedge q) \rightarrow (r \vee \sim s)$ is false,then the truth values of $p, q, r$ and $s$ are respectively:

Show that the following statement is true by the method of contrapositive.
$p:$ If $x$ is an integer and $x^{2}$ is even,then $x$ is also even.

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.

If $p, q, r, s$ are statements,where:
$p: A^2-B^2=(A-B)(A+B)$ where $A, B$ are matrices and $AB \neq BA$
$q: 5 \leqslant 5$
$r: { }^8 C_1+{ }^8 C_2+{ }^8 C_3+\ldots+{ }^8 C_8=256$
$s: \text{Maximum value of } { }^8 C_r \text{ is } 70$
Which of the following statements has a truth value of true?