Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 2 / d / i

Table of contents
- Solution i

Solution

There are

n^{2}

possible ordered pairs and hence

2^{n^{2}}

binary relations. A reflexive relation must contain the

n

diagonal pairs, while its remaining

n^{2} - n

pairs are unrestricted. Subtracting the reflexive relations gives

2^{n^{2}} - 2^{n^{2} - n}

binary relations that are not reflexive.

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