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

written 9.2 years ago by teamques10 ★ 70k

modified 4.1 years ago by krithikkm200 • 10

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: May 2014

discrete mathematics

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written 9.2 years ago by teamques10 ★ 70k

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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