Q24 of 109 Page 1

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is

∵ An important property of equivalence is that it divides the set into pairwise disjoint subsets called equivalent classes whose collection is called a partition of the set. Note that the union of all equivalence classes gives the complete set.

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22

Let R be the relation on the set A = {1, 2, 3, 4} given by

R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then,


 23

Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is

 25

S is a relation over the set R of all real numbers and its is given by (a, b) ϵ S ⬄ ab ≥ 0. Then, S is

 26

If the set Z of all integers, which of the following relation R is not an equivalence relation?