Question

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (C)

7

Answer 2

R is reflexive if it contains (1, 1), (2, 2), (3, 3)

$( 1,2 ) \in R , ( 2,3 ) \in R$

$R = \{ ( 1,1 ) , ( 2,2 ) , ( 3,3 ) , ( 2,1 ) , ( 3,2 ) , ( 2,3 ) , ( 1,2 ) \}$R will be

transitive if (3, 1); (1, 3) ∈ R. Thus, R becomes an equivalence relation by adding (1, 1) (2, 2) (3, 3) (2, 1) (3,2) (1, 3) (3, 1). Hence, the total number of ordered pairs is 7.