3. Let {B;}je1 and {C;};e1 each be a family of mutually disjoint sets. If B; = C; for each i e I, prove that UB: UCi. ieI ieI

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: Let A = {x € N|x < 7}, B = {x € Z] -4 < x-2<4}. And C = {x E R|x² + x - 12 = 0}. a) List the…

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Q: Let A. B and C be sets. In each part, either prove the statement or give a counterexample. (a) AUBCC…

A: Given: A, B, and C are sets. We have to either prove the statement or give a counterexample. (a)…

Q: I don't understand why you put Ui element of I. I think you made a mistake. Please let me know.…

A: Step 1:Step 2:Step 3:Step 4:

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (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: Let A and B be sets. Prove that A c B if and only if A NB = A.

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Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

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: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: Consider S to be the universal set. Let X = (AUB) nC and Y = (AnT)U (An B). %3D Write out the…

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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: For any sets A, B, show that (A \ B)c = Ac ∪ B.

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Q: A – Ö B, = Ü(A – B.). Ü(A – B;). i=1

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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: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

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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: SETS Prove that X ⊆ Y if and only if X ∪ Y = Y.

A: Draw a sets of X and Y and plot different cases and check all conditions having XUY=Y.

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

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: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

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

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Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…