5. Prove the following statements. (i) Let f: A B and g: B-C be two functions, If g of is onto, then g is onto. ・ got (x₁) = got (x₂) Assume qf (x₁); Proof we only need to prove x₁ = x2 #f(x₂) since by def (gof) (x₁) = got (X₂) implies g (f(xi)) = g(x₂))) we see that f(x₁) = f(x₂) which implies x₁ = x₂ because gis is onto. By definition we have got is (ii) Let A, B, and C be three sets, then An (B-C)=(ANB) - (ANC). (iii) (AUB) - B=A-(ANB). is onto is onto.

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