When A and B are sets, and x is an element of the universal set, the property “x ∉ A − B” is valid if and only if

Q: a) Does B – A = C – A imply that B = C? Justify b) Next, does A – B = A – C imply B = C? Justify c)…

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Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: Give examples of the following, and provide justification as to why your answers are examples of the…

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Q: If R is the universal set, find: 1. Q ∩ R 2. Z ∩ I 3. N ∩ I

A: Since R is universal set.

Q: State whether or not each of the following sets is closed under the operations of addition and…

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Q: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

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Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: a) Does B - A =C – A imply that B = C? Justify b) Next, does A – B = A – C imply B = C? Justify c)…

A: A-B=x∈A and x∉B = A∩Bc

Q: Extra Credit. Let A and B be (not necessarily finite) sets. Prove that if A = B, then P(A) × P(B).

A: Let A and B be any two sets which are not necessarily finite sets. Prove that if A≈B, then PA≈PB.…

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: The boundary of a set is equal to the boundary of the complement True O False O

A: A point of a set is called boundary points if any neighbourhood of this point contains point of the…

Q: Which of the following statements is true about the three sets A.B.C defined below: A=[ – 4,4]…

A: The given three sets are: A=[-4,4]B=[-6,2]C=[-2,6] i.e. the set A consists of the elements…

Q: Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it…

A: Truth table for the symmetric difference is,

Q: a) Disjoint, non-empty sets A, B, and C such that Aº N (BUC)= A° Is there such an example?

A: Soln :- Disjoint, non-empty sets A,B & C such that  ACn (B∪C)=Ac Yes,      One can always find…

Q: True or False For sets A and B, if AcB, then An B = A O True O False

A: Given A ⊂ B

Q: If ? = {₤,₱,$, ¥} and ? = {♥, ♠, ♦, ♣}, which of the following statement(s) is/are NOT true? i. The…

A: If there are two sets - set Aand set B Equivalent sets are sets if there are same number of elements…

Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: For all sets A, B, and C, An (BU C) = (A N B) U (AN C). Fill in the blanks in the proof for the…

A: The union of two sets contains all the elements contained in either set . The intersection of two…

Q: Which of the following statements on sets is FALSE? O a. AN A° = Ø O b. Equivalent sets are equal. O…

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Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

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Q: Which of the following sets is a universal set for the other four sets? O The set of even natural…

A: .

Q: Let A and be any sets. Mark the statement that is true OAUB CA OA - B C В В СВ O AC = { } = OANB C в

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Q: True or False: For sets A and B, if A cB, then A u B = A. True False

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Q: Determine if the following statements are true or false. Here A represents any set. (a) oCA (b) A'CA…

A: Here let us consider A to be any set which consists some elements U is a universal set  A' is a…

Q: Mark the statement which is TRUE. O A. AN (BUC)- (AU B)n (A UC). O B. if ANB= AUB, then A = B. U C…

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Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: If X = {£, P, $) and Y = {0,0,0), which of the following statement(s) is/are NOT true? i. The two…

A: The objects of the sets X and Y are totally different that is they have no common element as such.…

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

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Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

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Q: Consider the following statement. For all sets A and B,  (A − B) ∪ (A ∩ B) = A. An algebraic proof…

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Q: Which of the following statements on sets is FALSE? O a. AN AC = Ø O b. Equivalent sets are equal. O…

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Q: If X = {£, P, $} and Y = {0,©,0}, which of the following statement(s) is/are NOT true? i. The two…

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Q: Assume that the statement applies to all sets. Is it true or false? A – (BO C) = (A – B) (A – C) 2.

A: A-(B INTERSECTION) C= (A-B)INTERSECTION(A-C)

Q: Determine whether or not the following is true: for all sets A, B and C, (AUB) (C\A) = AU (B\C); If…

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Q: Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. Does…

A: The equality A∪B=A+B is not always true for every sets A and B. It is true only when A and B are…

Q: Match the following term with the appropriate description​ A-F below. Assume A and B are sets.   The…

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Q: Which among the statements below does not show the relationship between the intersection and union…

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Q: Which of the following statements is true OA. For all sets A, B and C, A- (B –C) = (A - B) -C- O B.…

A: Option B and E are correct.

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Prove or disprove the following statement: Let A, B, X be sets. If X ⊆ A ∪ B, then X ⊆ A or X ⊆ B.

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Q: Are the following pair of sets equal? Justify your answer? A = { x:x is a letter in the word FOLLOW}…

A: Set: A set is a well-defined collection of distinct objects. Equality of Sets: If two sets A and B…

Q: se an element of argument to prove for all sets A,B,C (A-B)∩(C-B) = (A∩C)-B please explain if…

A: Let A, B, C are the three sets which can be assumed as,  A=1, 2, 3, 4 B=3, 4, 5, 6 C=1, 2, 3, 7, 8…

Q: point the step in the argument that is not valid and explain why ? Theorum: For all sets A,B   A’∪B’…

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Q: (X – Y)n (Y – X) = Ø

A: To determine the truth of the statement: (X-Y)∩(Y-X)=∅ where X,Y and Z are subsets of a universal…

Q: our answer Prove or disprove For all sets A. B and C, ir ABOC-0, then A. B and C are UD. AN, A.A-B.…

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Q: Use an element argument to prove the statement that for all sets A, B, and C, if A ⊆ B then A ∪ B =…

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Q: For all sets A, B, and C. Is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement. You may justify…

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Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.

A:

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”.