(a) For all sets A, B, andC, if A ⊆ B and A ⊆ C, then A ⊆ (B ∩ C).

Q: (3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nC =A…

A: Explanation A and B:

Q: 1. If A and B are sets, show that AB if and only if AUB=B. 2. If A and B are sets, show that AB if…

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Q: IF A and B are sets then A-BC A UB

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Q: QUESTION 19 Match the set operation with its definition. B ANB B AUB 8 AC a. {x|x €A and x EB} b.…

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Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: (3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nc =…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: QUESTION 3 Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C)U(B – C) by using…

A: To prove the equality of A∪B-C=A-C∪B-C it is enough to show that  A-C∪B-C⊆A∪B-C and…

Q: Below are two sets, one of all presidents of the United States and one of all veeps (vice…

A: The given two sets are: presidents ={'George Washington', 'John Adams', 'Thomas Jefferson', 'James…

Q: QUESTION 4. Let A, B, and C be three subsets of non-empty universal set U, and let S = (A-B)U(BUC)…

A: Let's solve which sets are not equal to S.

Q: if A ⊆ B and C ⊆ B^c , then A ∩ C = ∅.

A: Given that A⊂B and C⊂Bc.We need to prove that A∩C=∅. On the contrary assume that there exists x such…

Q: QUESTION 5 Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C)U(B – C) by using…

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Q: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =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: 1. Let A, B, and C be sets. Given A C B, show that (a) AnC C BnC. (b) ВС А.

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Q: Let A, B, and C be non-empty sets. Then Cx BxA=C×A×B if and only if O A=B O A=B=C O None of these O…

A: We can tackle this problem easily by assuming some examples  case (i) Let A=B=C = {1,2} we have,…

Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

A: Given C and D are two subsets of universal set U.

Q: QUESTION 3 Let S = {Siyanda, Ayanda, Sunil, Mohamed}, T = {Sunil, Mohamed, Tebogo}, {Mohamed,…

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Q: Prove formally that A\ B= A\(An B), for any sets A and B.

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Q: Problem 2: Prove or disprove using an element-based argument: Given a universal set U, for all sets…

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

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Q: Problem 2: Prove or disprove using an element-based argument: Given a universal set U, for all sets…

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Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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Q: 1. Let A and B be sets. Prove that A C B if and only if An B=A

A: Prove that A⊂B if and only it A∩B

Q: QUESTION 18 True or False: The negation of an or statement is logically equivalent to the and…

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Q: A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B)…

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Q: Suppose A and B are sets. Prove that A – B = AN B.

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Q: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: Let A, B, and C be sets from some universe U. Prove by contradiction if A C B and BC C, then AnC=0.

A: Result: Let A is a set in universal set. If x is element in universal set then either x ∈ A or x ∈…

Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: Let A, B and C be sets. Prove that  A ⊆ B if and only if A − B = ∅,

A:

Q: QUESTION 6 Prove that for sets A, B and C, that A n (BUC) =(ANB)U (ANC) using just the basic…

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Q: Prove that if A and B are sets, then A - B = An BC.

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Q: QUESTION 1 For all non-empty sets A,B,C,D, it AXB =CxD, then A = Cand B = D. True False

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Q: QUESTION 11 Given the following Universal Set and associated sets within, answer the following…

A: We have to find all subset of A

Q: Rework problem 12 from section 1.2 of your text, about disjoint subsets A and B of a universal set…

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Q: Prove or disprove that for all sets A, B, and C, we have a) A × (B ∪ C) = (A × B) ∪ (A × C). b) A ×…

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Q: QUESTION 3 which of the following is the power set of the set S={ a, b, c}? {Ø,S} o{0,{a}, {b},…

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Q: QUESTION 2 Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9) and the sets A = {2, 4, 6, 8} and…

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Q: Let A,B be sets. Prove that AAB = if and only if A= B

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Q: et A = {a}

A: Given,        A = a

Q: Question 4 Let A, B be the subsets of some universal set &, (a) Draw a Venn diagram for the set BN…

A: As you mentioned.. I will solve 4) a )

Q: 1. Let A, B, and C be the subsets of U. Then by using laws of sets prove A-(BnC)=(A– B)U(A-C)

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Q: Let A, B, and C be sets. Prove that if A CB and B C C, then A C C.

A: Let, x belongs to A. Since, A is a subset of B, so, x belongs to A implies that, x belongs to B. So,…

Q: For any two sets A and B, if A=B,then A=B صواب ihi

A: Given a statement

Q: 1. For any sets A, B, and C; the distributive law states AU (B nC); that is a. (A U B) n (A UC) b.…

A: Let A, B, and C are three sets

Q: QUESTION 38 Use the Venn diagram to list the elements of the set in roster form. 12 11 13 15 14 17…

A: From the Venn diagram (A∩B) = {13,17}(A∩B)' means all the numbers outside of (A∩B).They are:…

Q: Question 2: Use set builder notations to prove that: a)X Y = (XUY) – (XnY), b)(Y – X) U (Z – X) = (Y…

A: Part(a) We have  by the definition of symmetric difference : X⊕Y=xx∈X-Y or x∈Y-X Now, we prove that…

Q: Let A, B and C be sets. Prove that  C ⊆ A ∩ B if and only if C ⊆ A and C ⊆ B

A:

Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

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

A: