Let S be a nonempty collection of subsets of R which is closed under set complements and set unions. That it, such that Ac ∈ S and A ∪ B ∈ S , for all A, B ∈ S . (a) ShowthatR∈S and∅∈S,usingthefactthatS ̸=∅. (b) ShowthatforallA,B∈S,(A\B)c ∈S andthenthat(A\B)∈S.

Q: I Let A = {1,3,5,7}, B = {1,2,3}, C = (6,7} and suppose the Universal set is U = {1,2,3, ..,7}. List…

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Q: Let T be the set of all TSU students. Determine if (T, R) a poset or not if R = {(a, b)|a ∈ T, b ∈…

A: 1 We  List all of the ordered pairs in the relation R = {(a, b)|a + b is even} on the set {1, 2, 3,…

Q: Argue that a set A is a Gδ set if and only if its complement isan Fσ set.

A: The given statement is of Baire’s Theorem.

Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: When is a set compact?

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Q: How do I write a set T such that S is an element of T and a proper subset of T?

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Q: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

A: It is given that the universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.If A = {1, 2, 3, 4, 5} and…

Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

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Q: Let A, B and C be subsets of a universal set U. Prove that (a) ACB if and only if An Bc = Ø. (b) An…

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Q: Let U = {a,b,c,d,e,f,12,13,14,15,16,17}, X = {a,b,c,15,16,17), and Y = {b,d,f,13,15,17}. List the…

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Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: QLet (X,t) be a topological space and A,E are two subsets of x show that : 3. A is closed set iff A…

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Q: B. Let B and C be the subsets of some universal set X, then prove that (C – B)' = BU C'

A: let B and C be the subsets of some universet x1 then prove that (c-B)' = BUC'

Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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Q: Let A, B be non-empty bounded sets, and A Ç B (A is a proper subset of B). Then sup A < sup B. True…

A: Let A=(1,2] and B=[1,2]

Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: Let the universe of elements include these letters: p, q, r, s, t, u, v, w, x, y. The first set A…

A: The universe set contains the elements: p, q, r, s, t, u, v, w, x, y The set A contains the…

Q: Prove that: (i) A is closed. (ii) A = nc. ก ACC closed (iii) A is the smallest closed set in X that…

A: Given the set A which is the closure of the set A, i.e. a set that contains all point of A as well…

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: 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: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

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Q: Let A, B, C be non-empty subsets of the universal set U such that (An B) CC. Prove that AC BUC.

A: Let x∈A, then either x∈B or x∉B.Case 1: If x∈B ⇒x∈B∪C.⇒A⊆B∪C.

Q: Let S be a set and let {A, | i E I} be a collection of subsets of S. Prove that UA, CS. ¡El

A: Given that S be a set and let {Ai | i belongs o I} be a collection of S.

Q: Let the universal set U, and the subsets of U are A = {x]x is a letter of Almutasim name},…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: Construct an example of a subset B of p({a, b, c, d}) such that (B, C) is a totally ordered set.

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Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: We have given the following n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60.

Q: 6. The following statements about sets are false. For each statement, give an example, i.e., a…

A: What is Counter Example: A counterexample is an illustration that meets the criteria for a…

Q: Let {Aa: a E I} be an indexed family of sets and let B be a set. Prove: (Uael Aa) nB = Uael( Aan B)

A: