7. (10 points) Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it.
(a) Suppose $a, b \in \mathbb{N}$. If $a \mid b$ and $b \mid a$, then $a = b$.
(b) For every natural number $n$, the integer $2n^2 - 4n + 31$ is prime.
(c) There exist prime numbers $p$ and $q$ for which $p - q = 95$.