Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which can be added to R to make it an equivalence relation is
(a) 2
(b) 3
(c) 5
(d) 7
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Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which can be added to R to make it an equivalence relation is
(a) 2
(b) 3
(c) 5
(d) 7
Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which can be added to R to make it an equivalence relation is
(a) 2
(b) 3
(c) 5
(d) 7
(d) 7
A = {1, 2, 3}.
R = {(1, 2), (2, 3)}
To make R an equivalence relation, it should be:
(i) Reflexive: So three more ordered pairs (1, 1), (2, 2), (3, 3) should be added to R to make it reflexive.
(ii) Symmetric : As R contains (1, 2) and (2, 3) so two more ordered pairs (2, 1) and (3, 2) should be added to make it symmetric.
(iii) Transitive: (1, 2) ∈ R, (2, 3) ∈ R. So to make R transitive (1, 3) should be added to R. Also to maintain the symmetric property (3, 1) should then be added to R.
So, R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (2, 1), (3, 2), (1, 3), (3, 1)} is an equivalence relation. So minimum 7 ordered pairs are to be added.