ISRO | ISRO CS 2017 | Question 1

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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