Which of the following are equivalence relations on $\mathbb{R}$?\\
(A) $a \sim b$ if and only if $|a - b| \leq 25$;\\
(B) $a \sim b$ if and only if $a - b$ is rational;\\
(C) $a \sim b$ if and only if $a - b$ is irrational;\\
(D) $a \sim b$ if and only if $f(a) = f(b)$ for every continuous $f : \mathbb{R} \longrightarrow \mathbb{R}$.