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25 August, 05:50

Prove that a relation that is reflexive and symmetric need not also be transitive.

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  1. 25 August, 09:33
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    We give a counterexample:

    Let R={ (a, a), (a, b), (b, a), (b, b), (c, c), (b, c), (c, b) } be a relation.

    It is reflexive as it contains (a, a), (b, b) and (c, c).

    It is symmetric as (a, b) and (b, a) are both in R; (b, c) and (c, b) are both in R.

    But it is not transitive, as (a, b) and (b, c) are in R, but (a, c) is not.
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