1. If A ana B are sets, show that Ac B if and only if An B = A.

Q: (a). If S1,, Sn are open sets in C, then so is Sk. =D1

A:

Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

A:

Q: Let ? = {1, 2} and ? = {1, 2, 3}. List all the elements in the set (? × ?) ∩ (? × ?)

A: A = {1,2} and, B = {1,2,3} So, A×B = {(1,1,), (1,2), (1,3), (2,1), (2,2), (2,3)} &, B×A =…

Q: If A and B are sets, and A = B, then A and B cannot be disjoint. True False

A: Given that If A and B are sets and A=B then A and B cannot be disjoint.

Q: 1. Let A, B abd C be sets. Prove that Au (B-C) = (AUB) - (C-A).

A:

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…

A:

Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: Suppose A and B are sets. Au B = B if and only if As B. True False

A: Given statement is A and B are two sets. A∪B=B if and only if A⊆B. We know that if A⊆B and B⊆A then…

Q: Draw a Venn diagram where U is set of all AKC purebred dogs, H={x/x is a herding dog} and B={collie,…

A: Given: U is the set of AKC purebred dogs. H = {x|x is a herding dog} B={collie, sheltie, Border…

Q: Let A,B,C and D are any sets then prove: If A C C and B c D then A U B CCUD.

A:

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

Q: Show by membership that for all sets A, B and C: A-(ANB) CA-B

A: Sets and relations

Q: For any sets A and B, which statement is false? OA NA = {} OAUB CANB OAN BC B OA CAUB

A: Remark:  We know that The union of two sets A and B is the set of all those elements which are…

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: Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser…

A: We used the concept that if a set contains n elements then it power set contains 2n elements .

Q: Draw a Venn diagram to show the set  An(B U C')

A: Furst find B U C' then An(B U C').

Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: Given the sets A, B and the universal set U, and that A and B are not disjoint, draw a Venn diagram…

A: It is provided that A, B are two sets that are not disjoint and U is the universal set. We need to…

Q: For all sets D, E and F, if D- FCE-F then DUF CEUF.

A:

Q: If Set A = {M,I,C,H,A,E,L} and Set B = {J,O,R,D,A,N}, what is A ⋃ B?

A:

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: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

A:

Q: in a venn diagram with two overlapping sets there are

A: Let define the two events A and B.

Q: 19. If A={People who live in Colorado} B={People who live in Denver}, draw a Venn diagram relating…

A:

Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

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Q: Let A, B, and C be any sets. Mark the statement that is false O A U (BUC) (AUB) UC OACUCC (An C)c OB…

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Q: Here is a Venn Diagram with sets B, D, and the universal set U. RODI

A: Given that  Venn diagram of with sets B,D and the universal set U.

Q: For any sets A and B, (AU B)

A:

Q: Let A, B and C be any three sets. Then Ax (BUC)=

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Can you conclude that A = B if A, B, and C are sets such thata) A ∪ C = B ∪ C? b) A ∩ C = B ∩ C?c) A…

A: According to the given information, it is required to conclude that A = B if A,B,C are sets such…

Q: Suppose A, B, and C are sets. Prove that (AU B) – C C AU (B – C). - -

A:

Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

A: Let A, B, and C are sets. Now we prove that A∪B∩C and C-A∪B∪(B-(A∪C)) are disjoint.

Q: Show by membership that for all sets A, B and C A - (AnB) CA-B

A:

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Consider sets A={1,3,5} and B = {2,4,6}. Find A U B

A: The given sets are A={1,3,5} and B = {2,4,6}. The union of any two sets is the set of all the…

Q: Refer to the Venn diagram below. How many elements are in the set AUB? nAUB) -

A: Given,

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: Let A, B and C be sets. Prove that CCANB if and only if C CA and CC B.

A: Consider the given information: Let A, B and C be sets. To prove that C⊂A∩B if and only if C⊂A and…

Q: 1. Are the two sets (An B)UC and A - (Bn C) the same set? Use Venn Diagram shadings to prove your…

A: As per our Bartleby guidelines, we are allowed to answer one question per query, Please ask Q2 as a…

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

Q: The Venn diagram shows sets A, B, C, and the universal set U.

A: Given Venn diagram:

Q: 2. Draw a Venn diagram for the set AU(BnC).

A: We first draw U, A, B, C

Q: Show that if A and B sets then A – B = ANB

A:

Q: The Venn diagram shows sets A, B, C, and the universal set U. Shade (CnA)'U B on the Venn diagram.…

A: Venn Diagram

Q: Let at AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9} and let the universal set U be all positive integer…

A: From the information, AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9}, U={all positive integer less than or…

Q: Let A, B,C be three sets. Show that if BC A and CCA\B, then BC A\C.

A:

Q: If Q, R, S are sets then QU(ROS) and (S-(QUR)) U (R- (QUS))) are disjoint sets.

A: This is a problem of the set theory. Two sets QU(R∩S) and ((S-(QUR))U(R-(QUS))) are given. The…

Q: Consider sets A={1, 3, 5} and B={2, 4, 6}. Find An B. {} {0} O {A, B} O {1, 2, 3, 4, 5, 6}

A: We have A = {1, 3, 5} and B = {2, 4, 6}.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.