7. (i) Show that the countable union of countable sets is a countable set. Give an example of such a set.

Q: Use the set definitions A = {a,b} and B = {b,c} to express the elements of the power set P(A ∩ B)…

A: We Know that A Power set is set of all subsets, empty set and the original set itself.It is denoted…

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Define Open set ?

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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: True or false? A∩(B∪C)=(A∩B)∪(A∩C) You should determine this by building the Venn Diagram for each…

A: Given statement is A∩(B∪C)=(A∩B)∪(A∩C)

Q: For each condition below, give an example of a set that satisfies that condition, or prove that one…

A: The given of the question is a list of conditions related to sets and subsets of real numbers, and…

Q: If a set is empty then number of subsets

A: Given : Empty set :   It is the unique set which does not contain any element is called as empty set…

Q: 26

A: The objective is to find an infinite collection of closed sets whose union is not closed.

Q: Give example open set is compact

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Q: Let & = (A xEA) be a family of sets, and let B be a set, Then B- (UA) = U (B-A). «ΕΔ a EA True False

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Q: The following is a proof that ``For all sets A and B, P(An B) ≤ P(A) ʼn P(B)". Fill in the blanks.…

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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: What is meant by the Cardinality of a finite set? Give one example.

A: The cardinality of a set is meant by the number of elements of the given set. If the set has no…

Q: (b) Use set theoretic notation to describe the set of all students that were only satisfied with…

A: Given: Venn diagram of given information is given below:

Q: Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of…

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Q: (iv) Show that for a countable set B, m*(AUB) = m* (A).

A: Given the a set B is a countable set and the equation m*(AUB)= m*(A) to be proved.   We know that…

Q: Give an example of a bounded set that has infinitely many isolated points

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Q: two example of open set in R, closed set in R, and the closure of that set

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Q: (1 point) Suppose that {A, B, C'} is a partition of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, where A…

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Q: Give an example of a countable collection of finite sets whose union is not finite.

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Q: Question 12 Select all that are True. A. O |P(A) × P(B)| = |P(AU B)| for all pairs of sets A and B…

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Q: A set A has 7 elements. Is it a powerset of another set? That is, is there a set B such that A = 2B?…

A: A set A has 7 elements. It cannot be a power set of another set. Since the cardinality of the power…

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

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Q: Answer the following True or False. (a) {1,2,3} is a subset of {3,2, 1, 4). (b) (3,2, 1,4) is a…

A: We have to find given statements are true or false.

Q: 4. Which of the intervals (-3, 3), [4, 7], (-4, 5], (0, ∞) and [0, ∞) are open, closed, both, or…

A: given some intervals to identify whether open, closed, both, neither

Q: Prove that an enumerable set is infinite.

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Q: Consider the following families of sets indexed by the set of natural numbers. i which among these…

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Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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Q: Which of the following statement is not true? * Disjoint set is a set which contains all objects.…

A: Disjoint set is the set which do not contain common points

Q: In a machine company, at least 45% of the machines produced per month do not pass the finish test…

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Q: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: show vacuous proof of statement that "empty set is a subset of any set"

A: