Q.
Let R = {(2, 3), (3, 4)} be relation defined on the set of natural numbers. The minimum number of ordered pairs required to be added in R so that enlarged relation becomes an equivalence relation is :
3552
179
Relations and Functions - Part 2
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Solution:
We know that a relation is an equivalence relation if it is reflexive, symmetric and transitive.
For reflexive relation (a,a)∈R
For symmetric: If (a,b)∈R, then (b,a)∈R
For transitive relation:
Let (a,b)∈R and (b,c)∈R, then (a,c)∈R ∴ Required R={(2,3),(3,4),(2,2),(3,3),(2,4),(4,2),(3,2),(4,3),(4,4)}
So minimum number of ordered pairs to be added =7.