Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 1 / c / i

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- Solution i

Solution

True. Fix

a \in A

. Reflexivity supplies

a R_{1} a

and

a R_{2} a

. In the definition of composition of relations, choose the intermediate element to be

a

itself. Then

a (R_{2} \circ R_{1}) a

. This holds for every

a \in A

, so the composite binary relation is reflexive.

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