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Question

If R is the largest equivalence relation on a set A and S is any relation on A, then
(a) R ⊂ S
(b) S ⊂ R
(c) R = S
(d) none of these

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Solution

(b) S ⊂ R

Since R is the largest equivalence relation on set A,
R A × A

Since S is any relation on A,
S A × A

So, S ⊂ R

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