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Question

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


Solution

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

(1,2)R,(2,3)R
 For R to be symmetric (2,1) and (3,2) should R

Now, R={(1,1),(2,2),(3,3),(2,1),(3,2),(2,3),(1,2)}
R will be transitive if (3,1) and (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, minimum number of ordered pairs required to make the given relation equivalance is 7.

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