Given two relations R, S on a Set X (so that R, S ⊆ X . X) : Prove or disprove, If R and S is transitive, then so is R ∪ S

Question

How would I go about solving this problem? Usually there is some set A, where you could deduce transitivity. But This is on the relation X times X

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score 2 · Accepted Answer · answered Sep 01 '20 at 07:21

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A binary relation $R$ on a set $X$ is a subset of $X\times X$.

The relations $R = \{(1,2)\}$ and $S=\{(2,1)\}$ are transitive, but the union $R\cup S = \{(1,2),(2,1)\}$ is not since $(1,1)$ and $(2,2)$ are missing.

answered Sep 01 '20 at 07:21

Wuestenfux

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Given two relations R, S on a Set X (so that R, S ⊆ X . X) : Prove or disprove, If R and S is transitive, then so is R ∪ S

1 Answers1