Let A, B, and C be sets. Prove the following statement: (A − B) ∩ (C − A) = ∅
Let A, B, and C be sets. Prove the following statement: (A − B) ∩ (C...
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.
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 sets. Assume A ⊂ B ⊂ C, prove C \B = C \(A∪B)
Let A, B, C, D be sets. Prove that if |ACand BD], then
Questions: 1. Let P be the statement: "For all sets A, B and C. if AUB CAUC then B - ACC." (a) Is P true? Prove your answer. (b) Write out the converse of P. Is the converse of P true? Prove your answer. (c) Write out the contrapositive of P. Is the contrapositive of true? Explain.
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)
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