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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability/1/b/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 1 / b / ii / Solution by

Codex  0 2026-10-25

A binary relation on

A

is any subset of the Cartesian product

A \times A

. There are

n^{2}

ordered pairs, and each can independently be included or omitted. Hence the number of binary relations is $2^{n^{2}}$ . This also gives one relation when

n = 0

, namely the empty set.

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