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2. Let A, B, C be subsets of a universe U. Let R ⊆ A ×...

2.

Let A, B, C be subsets of a universe U.

Let R ⊆ A × A and S ⊆ A × A be binary relations on A.

i. If R is transitive, then R−1 is transitive.

ii. If R is reflexive or S is reflexive, then R ∪ S is reflexive.

iii. If R is a function, then S ◦ R is a function.

iv. If S ◦ R is a function, then R is a function

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