1.)
a) Disprove by giving a counterexample that for any sets A,B,C, A∩(B∪C) = (A∩B)∪C.
b) Prove that (B -A)∪(C -A) = (B ∪C)-A. First show that every element on the left side belongs to the right side, then show that every element from the right side belongs to the left side, using de?nitions of union and difference.
c) Let g: A → B and f : B → C be one-to-one functions, where A, B, C are arbitrary sets. Prove that their composition f ?g: A → C is a one-to-one function.