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Consider the two functions f : S → T and h : T → U for non-empty sets S,T,U Decide whether each of the following statements is true or false, and prove each claim.

a) If h ∘ f is injective, then f is injective.
b) If h ∘ f is injective, then h is injective.
c) If h ∘ f is injective and f is surjective, then h is injective.

Sagot :

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