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Archangel Macsika

Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive

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Consider the set \{a,b,c,d\} . Consider the relation.

R=\{(a,a),(b,b),(c,c),(d,d),(a,b),(b,a),(a,c),(c,a),(b,c),(c,b),(b,d),(d,b)\}

We can see that the relation is reflexive since every element of the set are related to themselves.

Also it is symmetric for every aRb,bRa and so on.

But, it is not transitive. We have (a,b) and (b,d) but no (a,d)

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