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 Incoming links: Union of antisymmetric relations

Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Discrete mathematics / 3 / b / Solution 2026-10-25

For a counterexample to closure under union of antisymmetric relations, take

A = {0, 1}

,

R = {(0, 1)}

, and

S = {(1, 0)}

. Each is an antisymmetric relation: neither contains an off-diagonal pair together with its reverse. But

R \cup S

contains both

(0, 1)

and

(1, 0)

while

0 \neq = 1

. Therefore $R \cup S$ is not an antisymmetric relation.

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