Suppose that A and B are disjoint finite sets. Prove that AUB is finite.

Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: Give two sets that are equal. Prove that they are indeed equal by using the "Axiom of…

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Q: Let A and B be finite sets with A - B = {a, b, c, d, e, f, g} and An B = {h, i, j, k, l, m}. Find…

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Q: Give an example of a set with a finite number of points that is not se-quentially compact, or else…

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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: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

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Q: Prove that (2,5) is an open set

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

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Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Prove that the unoin of a finite number of bounded sets is bounded.

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Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

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

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Q: Prove. Power set of a null set is empty.

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Q: Prove that an enumerable set is infinite.

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Q: How to Apply the Archimedes'principle to prove that a set is empty

A: Consider the given information. the Archimedes' principle is defined as, Property states that for…

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

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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: 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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Q: Suppose that A and B are finite sets. Prove that AxB is finite.

A: Result 1 :  A be an non-empty finite set if and only if cardinality of A is a finite natural number…

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

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Q: Show that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

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Q: Suppose A,B and C are sets with C∕= ∅. Prove that if A×C= B×C, then A= B. Why is it necessary that…

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Q: Let A, B and C be finite sets with A C B. Suppose that B |C| =5, and that |BnC= 4. Decide whether…

A: Given: A⊂-B, |B| = |C| = 5 and | B∩C| = 4