If R is the largest equivalence relation on a set A and S is any relation on A, then
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

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