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

Q: Prove that the set {a E R: a2 not equal to 6} is open.

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Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: Let  X And Y are sets. Give a direct proof for X∩Y⊆X

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Q: A and B are bounded subsets of R, then prove that UB and AnB are bounded.

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Q: For any sets A, B, and C, prove that Ac Bnc if and only if A c B and A CC

A: Consider the statement,

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: Suppose A and B are subsets of a universal set U. Don't use Venn Diagrams to Show that…

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Q: Let A and B be sets. Suppose that A ⊆ B. Prove that P(A) ⊆ P(B)

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Q: B. Let B and C be the subsets of some universal set X, then prove that (C – B)' = BU C'

A: let B and C be the subsets of some universet x1 then prove that (c-B)' = BUC'

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

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Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

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Q: Let A and B be open sets in a topological space. Is A ∩ B open?

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Q: Let A and B be sets.                                   If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for…

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Q: Let A and B be finite sets such that B = {b1, b2}. Prove that |A – B| < |A|.

A: We are given that A and B are two finite sets, where B= {b1, b2}.We have, |B| = 2, and let |A| =…

Q: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: Prove that if X ∩ Y = X ∩ Z and X ∪ Y = X ∪ Z, then Y = Z for all sets X, Y , and Z.

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Q: prove that If A, B, C are finite sets such that An B n c = Ø, then | A U BUC| = |A | + | B | + | CI.

A: Solution is following in explanation step.

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

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Q: Let A be an uncountable set, and B a countable set. Prove that AUB is uncountable.

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Q: A∩((X−B)∩(X−C))=∅

A: We have to prove that A∩((X−B)∩(X−C))=∅ if and only if A⊂B∪C

Q: If A and B are bounded subsets of R, then AuRand AOR are bounded: prove that

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Q: Let A, B, C be non-empty subsets of the universal set U such that (An B) CC. Prove that AC BUC.

A: Let x∈A, then either x∈B or x∉B.Case 1: If x∈B ⇒x∈B∪C.⇒A⊆B∪C.

Q: Let A and B be sets. Let X = A n B, Y = A \ X and Z = B\ X. Prove that X n Y = Ø, X n Z = Ø, Y n Z =…

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Q: Let S be a set and let {A, | i E I} be a collection of subsets of S. Prove that UA, CS. ¡El

A: Given that S be a set and let {Ai | i belongs o I} be a collection of S.