An indexed family of sets (A,hcs is said to be a cover of a set X if and only if X CU,crA Use this idea to prove that if (Ches and (D,), are two different covers of a nonempty set A then (Gn DlneN forms a cover of A

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: 1. Let A, B abd C be sets. Prove that Au (B-C) = (AUB) - (C-A).

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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.

Q: 11.0, Prove that the interior of the interin of a set is equal to the interies of that set

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Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let A…

Q: Show

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

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: Theorem 1.10. A set is infinite if and only if there is an injection from the set into a proper…

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Q: Let A = {Ba: a € A} be a family of sets and let G be a nonempty set. Prove Gn an (UB.) - U(GOB₂) =…

A: Given: A=Bα : α∈∆ be a family of sets and let G be a nonempty set. To prove: G∩∪α∈∆Bα=∪α∈∆G∩Bα

Q: Let R be a relation on A. Then for all n ≥ 0, prove R^n is a set. (Discrete Mathematics, powers of a…

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Q: For every element r in A, there is an element y in B such that (x, y) is in F. Can you please…

A: Relation: The relation from a set A to a set B is a subset of Cartesian product A×B. Function: The…

Q: ieN 5. (a) Uli,i+ 1]= (b) Nli, ieN ieN 6. (a) | Iro.i +11=

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Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

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Q: For an indexed collection of sets to have an intersection an element needs to be in every set right?…

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Q: Prove that every nonempty subset of a well-ordered set is well-ordered.

A: Given problem is :

Q: Suppose A, B and C are sets. Prove that A\ (BC) = (AB) U (ANC). [Prove this using elements of these…

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Q: Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!.…

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Q: How can I show that the collection  A composed of empty set and all cofinite subsets of X Is a  sets…

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Q: Theorem 1.12. The union of countably many countable sets is countable.

A: We have to prove that the union of countably many countable sets is countable.