Let R={(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}.

Question

Let \(\mathrm{R}=\{(1,2),(2,3),(3,3)\}\) be a relation defined on the set \(\{1,2,3,4\}.\) Then the minimum number of elements, needed to be added in R so the R becomes an equivalence relation, is :

(1) 10

(2) 8

(3) 9

(4) 7
 

Answer 1

Correct option is (4) 7  

A = {1, 2, 3, 4}

For relation to be reflexive

R = {(1, 2), (2, 3), (3, 3)}

Minimum elements added will be

(1, 1), (2, 2), (4, 4) (2, 1) (3, 2) (3, 2) (3, 1) (1, 3)

\(\therefore\) Minimum number of elements = 7