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Prove the following: Theorem. Let R ⊆ X × Y and S ⊆ Y × Z...

Prove the following: Theorem. Let R ⊆ X × Y and S ⊆ Y × Z be relations. Then

1. Range(S ◦ R) ⊆ Range(S), and

2. if Domain(S) ⊆ Range(R), then Range(S ◦ R) = Range(S)

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