Show that if a relation on set A is transitive and irreflexive then it is asymmetric.

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Show that if a relation on set A is transitive and irreflexive then it is asymmetric.

written 7.4 years ago by

teamques10 ★ 65k

modified 2.3 years ago by

pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: May 2014

discrete mathematics

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written 7.4 years ago by

teamques10 ★ 65k

Suppose R is not asymmetric.

Then there exists a, b € A such that aRb and bRa.

As R is transitive, aRa.

As R is irreflective, this is not possible.

So R is asymmetric.

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