Let A,B and C sets. Assume A ⊂ B ⊂ C, prove C \B = C
\(A∪B)
Let A, B and C be sets. Prove
10. Let A, B, and C be sets. (a) Prove or disprove: if A - C CB-C, then ACB. (b) State the converse of part (a) and prove or disprove.
Let A, B, and C be sets. Prove the following statement: (A − B) ∩ (C − A) = ∅
Let A, B, C, D be sets. Prove that if |ACand BD], then
4. Let A, B, and C be sets. Prove that AU(BNC) = (AUB) n (AUC).
6. (10 points) Let A, B, and C be sets. Prove (AuB)C(AnC) u(BnC)
Let A and B be sets. Prove the following statement: B ⊆ A if and only if ¬A ⊆ ¬B
Let A and B be sets. Prove the following statement: B ⊆ A if and only if A ⊆ B.
For nonempty sets A, B and C, let f : A → B and g : B → C be functions. Prove that if g ◦ f is injective, then f is injective
Problem 2. Let A, B be sets. Prove that if ACB, then P(A) CP(B). Explain why we can conclude that if A= B, then P(A) = P(B). Problem 3. Let A.B be sets. Prove that if P(A) CP(B), then ACB. Explain why we can conclude that if P(A) = P(B), then A= B.