For any collection a of subsets of X, there is ntaining a.

Q: What set is in another class of infinity that is bigger than R?

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Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: Let A = {0,{1,2},3}. Make a list of all elements of A and a (separate) list of all the subsets of A.

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Q: Suppose that S is a non-empty finite set. Prove that ? has as many even-sized subsets as it does…

A: Let S be a non-empty set. Let A be the set of even sized subsets of S and let B be the set of odd…

Q: Show

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

Q: Exhibit a countable collection of open sets U; such that each open set OCR can be written as a union…

A: Given :- Uj is countable collections of open sets. To prove :Every open set O⊆ℝ can be written as a…

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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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. Find a set A such that A = {2, JA]}.

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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: Show that for any nonempty set A, there exists unique set B such that for any x. xEB ex belongs to…

A: From your question, it is clear that "A" is a set of sets, i.e., members of the set "A" are sets.

Q: Construct a family of sets that demonstrates R is not compact

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Q: 3. Let X be a set. Call a subset A C X to be finitely complemental if its complement is either…

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

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Q: Give an example of a countable infinite, sequentially compact subset of R.

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Q: Consider the set X={a,b,c,d} construct all the possible topologies of X that have only three open…

A: Given: The set X=a,b,c,d To find:  all the possible topologies of X that has only three open…