Question:
If R is the largest equivalence relation on a set A and S is any relation on A, then
(a) $R \subset S$
(b) $S \subset R$
(c) $R=S$
(d) none of these
Solution:
(b) $S \subset R$
Since $R$ is the largest equivalence relation on set $A$,
$R \subseteq A \times A$
Since $S$ is any relation on $A$,
$S \subset A \times A$
So, S ⊂ R