Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

Q: Prove: If A,B and C are sets, then A ×(B ∪C) = (A ×B)∪(A ×C).

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Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: For all sets A, B, and C, it holds that (An C) U (B \ C) = (B U C) \ (C \ A). True False

A: We have solve the set true and false

Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

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Q: What can you say about the sets A and B if A ⊕ B = A?

A: The symmetric relation is described as, A ⊕ B =(A-B) U (B-A)

Q: If A, B,C, and D are sets, does it follow that (A ⊕ B) ⊕ (C ⊕ D) = (A ⊕ C) ⊕ (B ⊕ D)?

A: The symmetric difference between the set is associative and commutative. So, (A⊕B) ⊕C=A⊕(B⊕C)…

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 X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

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Q: Use the Venn diagram shown to the right to determine whether the given sets are equal for all sets A…

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Q: What is the intersection of sets A and B?

A: The intersection of sets is a set which include the common of the two sets A and B. It is…

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

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Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

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Q: Let A, B, and C are three sets, prove that C × (AN B)' = (C X A') U (C × B') CS

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Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

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

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Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Show that for all sets A, B, and C, if A C BUC, then ANC + Ø or A C B.

A: In order to prove this we need to use the property that if X⊂(Y∪Z) ⇔X⊂Y or X⊂Z

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

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Q: Let A, B, and C be sets. Show that (A-B)-C=(A-C)-(B -C).

A: A, B, C are any set, we need to show that (A-B) - C = (A-B) - (A-C) this can be done using the…

Q: If A, B, and C are sets such that A ∩ B ≠ Ø and B ∩ C ≠ Ø, then A ∩ C ≠ Ø

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Q: or any of the sets id, bic it a,bsCthen a b anteo

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Q: If A and B are any two sets and AUB = . A n B, then

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Q: Prove by contradiction, for any sets A and B , if A CA- B, then An B = Ø

A: We want to prove if  A ⊂ A - B, then A ∩ B = ∅

Q: If S and T are two sets such that S has 21 elements, T has 32 elements, and   S ∩ T has 11 elements,…

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Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

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Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

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

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Q: When using Venn diagrams to verify or determine whether set statements are equal we use…

A: Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements…

Q: What is the union of sets A and B?

A: Assume the independent sets A and B. Set A = 0,1,2Set B = 4,5,6

Q: Decide which of the following represent true statements aboutthe nature of sets. For any that are…

A: (c) Given- A∩B∩C=A∩B∪C   To find- Whether the above statement is false or true. Concept Used- Using…

Q: Let A, B, and C be three sets. If A⊕C=B⊕C, show that A=B

A: Solution : Given that A,B and C are three sets. And the Direct sum of set A and C is equals to…

Q: Let the Universal Set, S, have 100 elements. A and B are subsets of S. Set A contains 42 elements…

A: To find the number of elements in A but not in B we need to subtract the number of common elements…

Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…

Q: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

A: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

Q: Show that if A and B are sets |A| = |B|, then |P(A)| = |P(B)|

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Q: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

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Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

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

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

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Q: Let the Universal Set, S, have 120 elements. A and B are subsets of S. Set A contains 92 elements…

A: Universal set s=120 elementsSet A=92Set =27elemants in  A and B=21

Q: If A,B and C are sets, then (AUB)-C=(A-C)U(B–C).

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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”.