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How many elements are there in the smallest equivalence relation on a set with 8 elements?

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How many elements are there in the smallest equivalence relation on a set with 8 elements?

(a) 10^2

(b) 8

(c) 48

(d) 32

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I would like to ask this question from Number of Relations topic in division Relations of Discrete Mathematics

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Right answer is (b) 8

Explanation: Let R is an equivalence relation on the set S with n elements and so it satisfies reflexive, symmetric and transitive properties. The smallest equivalence relation means it should contain minimum number of ordered pairs i.e along with symmetric and transitive properties it must always satisfy reflexive property. So, the smallest equivalence relation will have n ordered pairs and so the answer is 8.

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