Can you please provide the answers and explanations with them? Indicate which sets are disjoint to the given set. (Select all that apply.) AC ∪ BC   A ∩ B A ∩ BC AC ∩ B A ∪ B A ∪ BC AC ∪ B AC∩ BC AC ∪ BC None are disjoint   Find the indicated sets with A, B, and U defined below. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) U = {1,2,3,4,5,6,7,8,9,10}A = {1,2,3,4,5,6,7}B = {4,5,6,7,8} (a) AC ∪ BC= { }(b) (AC ∪ BC)C = { }   Find the indicated sets with A, B, and U defined below. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) U = {1,2,3,4,5,6,7,8,9,10}A = {1,2,3,4,5}B = {4,5,6,7}C = {5,6,7,8} (a) A ∩ (B ∪ C)= { }(b) A ∩ (BC ∪ C) = { }

Q: Let the Universal set be the letters a through j: U = (a, b, ..., i, j]. Let A = {b, c, d, j}, B =…

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Q: elements

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Q: Prove using the properties of set operations: a. A - B and An B are disjoint.

A: Solution-: We want to prove A-B and A∩B are disjoint.

Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {b, g, i, j}, B =…

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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: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {c, e, h, j}, B =…

A: Given : U = { a,b,c,d,e,f,g,h,i,j} A = { c,e,h,j }  B = {d,e,f,h}  C = { b,c,f,h }

Q: Give an example of each of the statements below using the sets indicated (and power sets) to show…

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Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

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Q: Which of the following statements are set identities? That is, which of the statements are true for…

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Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

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Q: 4. Prove or disprove For all sets A. B and C. if A OC-0,then A. B and Care your answers as ar AUD,…

A: The given statement is FALSE.

Q: Let the Universal set be the letters a through j: U= {a, b, ..., i, j}. Let A = {e, f, h, j}, B {d,…

A: Ans - Given,          The Universal set  U = {a, b, c, d, e, f, g, h, i, j}          A = {e, f, h,…

Q: Let the Universal set be the letters a through j: U = {a, b, .., i, j}. %D Let A = {a, d, f, g}, B =…

A: The universal set U is defined as, U = {a, b, c, d, e, f, g, h, i}.

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: Give an example of two sets that meet the following condition. If the condition is impossible to…

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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 or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: Let A, B and C are be sets. Show that we can have AnB= AnC without B=C

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Q: 6. Let A, B be finite sets. Show that if JA\ B| = |B\ AJ, then |A| = |B|.

A: The order of a set defines the number of elements of the set. For two finite sets A and B,…

Q: U is the universal set. A and B are subsets of U. n(U) = 30, n(A) = 13, and n(B) 12 n(A U B)' = 8…

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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: Suppose A and B are two sets such that ANB = Ø. Which of the following statements is/are true? (i)…

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Q: Sets B and D are subsets of the universal set U. These sets are defined as follows. U={f,k,m, s , y…

A: Given :U=f,k,m,s,yB=f,k,yD=f,k,m

Q: Here is a Venn diagram showing the sets C and D, as well as the universal set U. FU- gh ,y D- f Find…

A: a). D' = g, h, y, f

Q: Sets B and C are subsets of the universal set U. These sets are defined as follows. U={k, q,r,s, x,…

A: B ∩ Cl = {x | x ∈ B and x ∉ C)} Cl = { k, s, x} B ∩ Cl = { k }

Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. %3D Let A = {c, d, f, g}, B…

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Q: Let A, B, U and V be any sets such that A⊆U and B⊆V. Is (A×B)⊆(U×V)? Justify your answer

A: In the given question we have to justify that, is the set A×B⊆U×V where A⊆U and B⊆V. for the…

Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: Let A = {0, 1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}, and C = {0, 2, 4, 6, 8} e. Is there a pair of…

A: The given sets are A=0, 1, 2, 3, 4, 5, B=1, 3, 5, 7, 9 and C=0, 2, 4, 6, 8. e. Since the sets A and…

Q: 5. Write these sets in set-builder notation, where U = {1, 2, . . . , 20}. (a) {11, 12, 13, 14} %3D…

A: As per our guideline we are supposed to answer only three subpart of question you can repost other…

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

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Q: Find an example of sets A and B such that |A|=3,|A|=3, |B|=4,|B|=4, and |A∪B|=5.

A: Let A = {2, 3, 4} and |A|= 3 and B = {2, 4, 6, 8} and |B|= 4 The union of set A and B is the set of…

Q: Which of the following sets is NOT an empty set? Select one: a. The set of natural numbers less than…

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Q: If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :(i) A = {a, b, c} (ii)…

A: Given:

Q: Write out the indicated sets by listing their elements between braces. Suppose the Universal set is…

A: solution is given below

Q: Consider sets A = {2}, B = {2, 3}. a) If the universal set is Z, find i. P(A) N P(B), ii. A U Bº, i.…

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Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {e, f, h, j}, B =…

A: Ans - Given,            U = {a, b, c, d, e, f, g, h, i, j}           A = {e, f, h, j},  B = {d, f,…

Q: Let A and B be sets with A ⊆ B and B transitive. Prove that P(A) ⊆ P(P(B)).

A: To prove ''Let A and B be sets with A ⊆ B and B transitive. Then  P(A) ⊆ P(P(B)).'' We use the…

Q: What can you say about the sets if A×B Bx A You can choose more than 1 itemns! O a. A' B Ob. A or B…

A: We know that A×B={(a,b):a∈A, b∈B}B×A={(b,a):a∈A, b∈B}since A×B=B×A⇒(a,b)=(b,a)  for all a∈A, b∈B

Q: Give an example of each of the statements below using the sets indicated (and power sets) to show…

A: (a) If A belongs to B means A is the subset of B and B is a subset of C.

Q: re is a Venn diagram showing the sets B and C, as well as the universal set U. FU- -B- h,r ,Z nd the…

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Q: 4. Let the universal set U, and the subsets of U are A = {x\x is a letter of your first name}, (R my…

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Q: (e) (A-B)U (B-A) = AUB-AnB

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Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {b, e, f, i}, B =…

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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: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: We have to show that given relations is False.

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: Consider the sets to answer the following questions attached: A = {a, b, c, d, e, f, h, j} B = {a,…

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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”.