Find two infinite sets A and B so that A UB, AN B,А — В аnd B — А are all infinite sets. Show the elements in each of the above sets.

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: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

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Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

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Q: Find an example of nonempty, distinct sets A, B, C for which (ANB) UC = (AUB) nC.

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Q: Let + stand for the symmetric sum of sets, A+ B = (AU B) \ (A n B). Prove or disprove (A+ B)nC =…

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Q: Let A and B be subsets of a universal set U and suppose n (U) = 275, n(A) 100, п (В) = 70, п (An B)…

A: If A is subset of universal set U, then n( Ac ) =n(U)-n(A).

Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

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Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

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Q: Determine whether the set S = {1, x², 6 + x²} spans P2. S spans P2. O s does not span P2.

A: P2 is the vector set of all polynomials with real coefficients of degree 2 or less. So 1+x is an…

Q: For each n ≥ 3, find the number of subsets of {1, 2, . . . , n} of cardinality greater than 2 with…

A: Let X=1,2,3,....n The number of subsets of X with m elements is given by, Cmn

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: Complement: The complement of a set A is the set of elements in the universal set U that are not in…

Q: Identify each set as finite or infinite. Then determine whether 10 is an element of the set. \{x…

A: x:x is a fraction between 1 and 2

Q: about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of…

A: Let there are x elements in X2. So there are 6x elements in X1. There are 3x elements in X3. Given…

Q: rsection of any collection of com

A: This is a real analysis question. Let (X,d) be a complete metric space with X not ∅. Suppose the…

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 150, n(B) = 90, and n(A ∩…

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Q: Write a sentence of the form “. . ⊆ . . ” involving A, B, and at least two of the operations ∪, ∩,…

A: Given: A and B are any sets. To write: Sentence of the form “. . ⊆ . .” involving A, B, and at least…

Q: b. Define the finite and infinite sets in your own words and give example for each set.

A: We use the definition of finite and infinite set to answer the given question.

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

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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: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Prove that A is an infinite set if and only if ∀n ∈ ω, A has a subset B such that B ≈ n.

A: given that A is an infinite set let B be any set let prove this contradiction suppose assume that B…

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

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: Give an example of a set of numbers that is: a. Closed under both addition and multiplication. b.…

A: a. Set of real numbers b. Set of odd natural  numbers c. Set of irrational numbers

Q: Find the interior and boundary of the set: [0, 2] n [2, 4]

A: In the given question we have to find the interior and boundary of the set [0,2]∩[2,4]. Interior…

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

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Q: Fill in the blank so that the resulting statement is true. The number of distinct proper subsets of…

A: To fill in the blankThe number of distinct proper subsets of a set with n elements is ____

Q: Give an example of sets {An}n≥1 such that for each n ≥ 1, the set An ⊂ [0, 1] is both compact and…

A: Construct sets Ann≥1 such that for each n≥1, the set An⊂0, 1 is both compact and connected, but the…

Q: Give an example that achieves the following two infinite sets A and B with A C B and A - B.

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Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Find the complement of the set given that U={x xEI and -3<x<9}. (Enter your answers as a…

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Q: Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: A ∩ B ̸ =…

A: We have to give an example of 4 non-empty sets A, B, C, D such that all the following are…

Q: For every positive integer n, prove that a set with exactly n elementshas exactly 2n subsets…

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Q: Give an example of a set of numbers that is: a.Closed under both addition and multiplication.…

A: (a) Set X is closed under addition if any two elements x, y in X such that x + y in X  Set X is…

Q: supC = supA × supB.

A: This is a question from real analysis with usual topology.

Q: Specify the set A by listing its elements, where A = {x: x is a whole number less than 100 and…

A: As per out guidelines we can answer only 1 question. Please repost the remaining questions…

Q: If a set A has 6 elements, then the total number of possible relations on A is 262 260 62 26

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Q: Show that the set EE is: (ii). Closed iff E¯=E

A: Show that the set E is Closed iff E¯=E

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B

Q: Let A = { 0, 2, 4, 6, 8 } a. Determine whether each of the following is true or false: i. ii. 2 € A.…

A: We have to answer true or false and the description of A and possible lists of A.

Q: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

Q: Identify each set as finite or infinite. Then determine whether 10 is an element of the set. \{x…

A: Let the given set be A - A = x | x is a natural number greater than or equal to 10

Q: Identify each set as finite or infinite. Then determine whether 10 is an elementof the set. \{x \mid…

A: The given set is, natural number between 9 and 11

Q: Find n(A) for the set. A = {300, 301, 302, ..., 3000} %3D

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