(d) 7A = {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.