Question

LetA={a,b,c,d} write a relationon A which reflexive only

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Let A={a,b,c} and the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}. Then write minimum number of ordered pairs to be added in R to make it reflexive and transitive.

November 22, 2019

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Sourabh Thangavel

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ANSWER

Given the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.

Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.

The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.

Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)



∈A.

Now to make this relation to be transitive we are to add (a,c).

Then the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b),(a,c)}