Let A and B be subsets of a set X. Prove that if A ⊆ Bc, then A and B are disjoint.

Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Let A, B, and C be sets. Show that (A − B) − C = (A − C) − (B − C).

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Q: Let A, B, and C be sets (a) Prove that ACB iff A – B = Ø. (b) Prove that if A C BUCand ANB = Ø, then…

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Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: Let A and B be sets. Prove that A c B if and only if A NB = A.

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Q: Let A and B be two subsets of E. Prove using the set identities: А - В — В — А.

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Prove that for all sets A and B, A – B = AN B

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Q: Let A and B be sets. Prove that the intersection of A and B is is a subset of the union between A…

A: To show that the elements which are common to both A and B belong to either A or B.

Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

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Q: (ANB) –C= (A –C)NB.

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Q: Use an element argument to prove the following statement - Let A, B, and C be the sets. Prove that A…

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Q: Let A, B, and C be sets. Prove that: Ax (B\C) = (A × B) \ (A × C).

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Q: Find two sets A and B such that A E B and AB.

A: A=ϕ. And B={ϕ}Explanation:If you have any problem let me know here in comment box for this thankyou.

Q: Let A, B, C be sets. Prove A U (B and C) = (AUB) and (AUC)

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Q: Let A and B be sets. Prove that A union B = A intersection B if and only if A = B.

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Q: Let A and B be sets. Prove that A – B = AU B.

A: Let A and B be two sets. Now, A¯-B=A¯∩B¯ ⇒A¯-B=A∪B¯  by De Morgan's Law

Q: Let A and B be sets. Prove that A UB= (A – B) U (B – A) U (A N B).

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Q: Let S and T be two sets. If both S and T are countable, prove that S U T (the union of S and T) is…

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Q: Let A and B be sets. Prove that (A − B) ∩ (B − A) = ∅.

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