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If R and S are relations on a set A, then prove: R is reflexive and S is any relation implies RUS is reflexive.

If R and S are relations on a set A, then prove: R is reflexive and S is any relation implies RUS is reflexive.

Grade:11

1 Answers

Askiitians Expert Sahil Arora - IITD
19 Points
12 years ago

Dear Abhingya

R is reflexive ==> for all x belonging to A....x is related to itself

As both relations R and S are defined on A..

R union S is reflexive ==>for all x belonging to A....x is related to itself......which is true as R is reflexive.

Hence R is reflexive and S is any relation implies RUS is reflexive.

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Sahil Arora
IIT Delhi

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