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The number of equivalence relations of the set {3, 6, 9, 12, 18} is ______(a) 4(b) 2^5(c) 22(d) 90This question was posed to me by my school principal while I was bunking the class.This intriguing question originated from Closure on Relations in division Relations of Discrete Mathematics

Answer»

The correct answer is (a) 4

For EXPLANATION I would say: Number of equivalence RELATIONS are GIVEN by BELL number. The nth of these numbers i.e, Bn counts the number of different ways to partition a SET that has exactly n elements, or equivalently, the number of equivalence relations on it. Let’s say, 1 -> Equivalence relation with 1 element; 1 2 -> Equivalence relation with 2 element; 2 3 5 -> Equivalence relation with 3 element; 5 7 10 15 -> Equivalence relation with 4 element. Hence, the answer is 4.



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