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

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: AUB=ANB.

A: We have to prove the de Morgan's law: A∪B=A∩B By using the set theory.

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: 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: 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: 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: 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…

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”.