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ISRO | ISRO CS 2017 | Question 1
  • Last Updated : 14 Mar, 2018

Suppose A is a finite set with n elements. The number of elements and the rank of the largest equivalence relation on A are

(A) {n,1}
(B) {n, n}
(C) {n2, 1}
(D) {1, n2}

Answer: (C)

Explanation: An Equivalence relation is always Reflexive, Symmetric and Transitive, so for a set of size ‘n’ elements the largest Equivalence relation will always contain n2 elements whereas the smallest Equivalence relation on a set of ‘n’ elements contain n elements itself.
The Rank of an Equivalence relation is equal to the number of induced Equivalence classes. Since we have maximum number of ordered pairs(which are reflexive, symmetric and transitive ) in largest Equivalence relation, its rank is always 1. So option C is correct.

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