A set F is called an Fo-set (or an Fo) if it is a countable union of closed sets. Likewise, a set G is called a Gs-set (or a Gs) if it is a countable intersection of open sets. Then show that (a) [0, 1] is a Gs set. (b) (a, b] is a both Gs and an Fo set. (c) Q is an Fo set, but not a Gs set.

Q: Find an orthogonal set with the same span (and same number of elements) as 7 -5 4 4 7 (198) -10 -8…

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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.

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A: Take A as, 1,2,3 and B as 3,4,5 The cardinality of A and B is 3. Now let's define a function.

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Q: Show

A: We prove this statement by using definition of Borel Set.

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Q: 2. Let X= [0, 10] be the universal set and A = [1,4], B = (2,8), C = [3, 6) be the subsets of X.…

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Q: Prove that if A is transitive set, then A+ is also a transitive set.

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Q: Define Closed sets ?

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

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Q: (1) In the universal set U ={1,2,3,4,5} we define the following sets: A ={1,2,3}, B = {3,4}, and C =…

A: Note: You have posted a question with multiple subparts. We have solved the first three subparts for…

Q: (A – B) – C = A- (BUC)

A: Introduction :

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: Prove that the intersection of any two open sets is open

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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: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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Q: Show The union of a finite number of open sets in R is an open set.

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Q: (FNB) UC'

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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: A is an ordered pair (G,*), where G is a nonempty set and is a binary operation on G.

A: We can solve this as follows:

Q: Suppose that U1, U2, ..., Un is a collection of n open sets. Prove that their intersection…

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Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B).

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