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Assignment 2

If R1 ⊆ S × T and R2 ⊆ T × U are binary relations, the composition of R1 and R2 is the relation R1 ; R2 defined as: R1 ; R2 := {(a, c) : There exists b ∈ T such that (a, b) ∈ R1 and (b, c) ∈ R2 } (a) If f : S → T and g : T → U are functions is f ; g a function? (b) If R ⊆ S × S is transitive, show that R = R ∪ (R; R). (Hint: One way to show A = B is to show A ⊆ B and B ⊆ A. One of these directions is trivial.) Let R ⊆ S × S be any binary relation on a set S. Consider

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