Question

Let A = {1, 2, 3} number of non-empty equivalence relations from A to A are 

(1) 4 

(2) 5 

(3) 6 

(4) 8

Answer 1

Correct option: (2) 5 

The partitions far a set with 3 elements, {1, 2, 3}

{(1}, {2}, {3}} – Every element is in its own subset

{{1, 2}, {3}} – Two elements are together, one separate 

{{1, 3}, {2}} – Two elements are together, one separate 

{{2, 3}, {1}} – Two elements are together, one separate 

{{1, 2, 3}} – All elements are together in one subset 

∴ Therefore, total possible equivalence relation = 5