Recent content by fuzuli

I am stuck at a proof and do not even have an idea where to start and how to start: Let X and Y be sets, and let f : X → Y be a surjection. Prove that there is an injection g : Y → X such that f (g(y)) = y for every y ∈ Y. Could you please show me a way?

and for the second one: left to right: if m ∈ X\⋂At => m∈X and m∉⋂At => m∈X and m∉At for all t∈T => m∈X\At for for all t∈T. Therefore m∈⋃(X\At) right to left: if m∈⋃(X\At) => m∈X and (∃t∈T that m∈At or ∄t∈T that m∈At) if not for all t∈T, m∈At, then m∉⋂At...

Thank you so much for your instant reply. I think I understood your point. For example for the first one: left to right: if m∈ X∖⋃At => m ∈ X and m∉⋃At. so m∉At for all t∈At. if m∈X and m∉At for all t∈At, then X\At={m} for al t∈T then...

Hello there, I am extremely new to mathematical analysis and do not have an idea how to prove the following questions. Could you please give me a hand and show me a way? Let At , t ∈ T, be a family of sets, and let X be a set. Prove the identities...