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

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: Give an example of a set that satisfies the condition, or prove that one does not exist: An…

A: The statement or condition :An infinite intersection of non-empty closed sets that is empty.

Q: Let A and B be any sets (subsets of some universal set U). Use a proof by contradiction (and…

A: The given problem is to prove the following statement by contradiction method. In this method , we…

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: If AnB is pathwise connected set.  then A and B are:  a. Pathwise connected sets b. Not pathwise…

A: Pathwise connected means any two points in that set can be join by a continuous function. Roughly…

Q: Let A. B and C be sets. In each part, either prove the statement or give a counterexample. (a) AUBCC…

A: Given: A, B, and C are sets. We have to either prove the statement or give a counterexample. (a)…

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

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Q: Give two different but equivalent definitions for a set CCR" to be closed, and prove they are…

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Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: You are given two sets such that a set is not a subset of other. If you have to prove this,how do…

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Q: Here is a conjecture: Card (A - B) = Card(A) - Card (B) Decide whether this conjecture is true or…

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Q: If a universal set contains 250 elements,

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Q: Let A and B be sets. Suppose that A ⊆ B. Prove that P(A) ⊆ P(B)

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Q: The empty set is a proper subject of every set. true or false

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

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

A: Here are given sets A and B are finite sets. Then A=m, B=n  where m, n any fixed positive integer.…

Q: Let A and B be two sets. a) Suppose that A and B are both countably infinite sets. Prove that there…

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Q: 2 of 4 02 (Core): I can represent a set in roster notation and set-builder notation; determine if an…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: There are 320 martians traveling together in a spaceship and 128 of them are Male. (*Note: There are…

A: Given Information: Number of Martians is 320 Out of which 128 are male Of the male Martians 56 have…

Q: For all sets A, B, and C, A, B, C- AU (B-C) = (AUB) - (AUC). Your answer cannot be

A: Given: Universal set: U=1,2,3,4,5 Statement: A∪B-C=A∪B-A∪C To give: A counter example to disprove…

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

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 every Union of Open sets is also Open.

A: To prove: Every Union of Open sets is also Open.

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

Q: Let A be the set students who live on campus and let B be the set of students who walk to classes.…

A: The set: A-B contains all the elements that are present is set A but not in set B. The set: A'…

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

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Q: Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: A ∩ B ̸ =…

A: We have to give an example of 4 non-empty sets A, B, C, D such that all the following are…

Q: Consider two sets A and B defined in the universal set U. Set A contains elements that are prime…

A: Prime numbers less than 20 (Set A): A prime number is a natural number greater than 1 that has no…

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

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.