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The rank of smallest equivalence relation on a set with 12 distinct elements is _______

(a) 12

(b) 144

(c) 136

(d) 79

The question was asked in an international level competition.

This intriguing question originated from Number of Relations in chapter Relations of Discrete Mathematics

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The correct answer is (a) 12

To explain I would say: In the case of smallest equivalence relation, each element is in one equivalence class like {a1}, {a2}, … are equivalence classes. So, the rank or number of equivalence classes is n for a set with n elements and so the answer is 12.

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