 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/discrete-mathematics-continuous-mathematics-and-probability/1/c/iii/solution

False. Use the same two equivalence relations as in part (ii). They are both symmetric relations. The composite contains

1 S 3

, since

1 R_{1} 2

and

2 R_{2} 3

. It does not contain

3 S 1

, as shown there. Hence composition of relations need not preserve symmetry of a relation, even when both factors are also reflexive and transitive.

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