 Solution

ID: 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

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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