Prove that intersection of any class of convex subsets of N is convex?

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: Cantor set is measure at 1

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Q: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

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Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

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Q: True or false? For all sets A and B,  (A∪B)'=A'∪B' This can be determined by constructing a…

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Q: Show

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

Q: Prove that B = (0,1) is NOT a compact set.

A: To prove that (0,1) is not a compact set.

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: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

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Q: Prove that the set Q \ Z is countable.

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Q: Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

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

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Q: The set {(x,x) x+x≤1) is a Convex set Open set Disconnected set None of the above is a(an)

A: The given set is {(x1,x2) | x12+x22≤1} Clearly, this set represents the points of unit closed disc.…

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: Prove directly that the union of two disjoint sets, where one is countably infinite and the other is…

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Q: Prove that the set X = (18, 19) U [21,23] C R is NOT convex by using convex combination. Other…

A: The set is:

Q: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

A: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

Q: Prove that the set of all finite subsets of ω is countable. (Set theory)

A: The objective is to prove that the set of all finite subsets of ω is countable.