The union of the universal set and any of its subset is * none of the choices cannot be determined the complement of the universal set O the universal set itself O an empty set

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: let S = { 1, 2, 3, 4, 5, 6} How many subsets are there of cardinality 4? how many subsets of…

A:

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | x is a…

A: In roster notation, all the elements of a set are listed. In this notation each element is separated…

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: i. Provide an example to prove that the arbitrary intersection of open sets is not an open set ii.…

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Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A: The interval is (0,1) To construct Cantor's set.

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: Define Open set ?

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Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: Let A=(1, 2,3,4,5,6,7,8,9,10,11,12) how many different non-empty subsets are there in set A

A: Given,            A=(1, 2,3,4,5,6,7,8,9,10,11,12) We have to determine the number of different…

Q: Specify the set by roster.

A:

Q: Let A = {distinct letters occurring in the word HIPPOPOTAMUS}. What is |A|, the cardinality of the…

A: Cardinality of a set is defined as the number of distinct element in that set.

Q: 8. Disprove that every compact set has only a finite number of isolated points. V Note that the…

A: Let C be the compact set.If possible suppose that 'C' has a infinitely many isolated points. say…

Q: Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who arein school hockey team. Let Y…

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Q: 3.1 Show that a finite intersection of closed sets is closed.

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Q: True or False: If a set contains ∅ as an element, it cannot be a partition of another set. Please…

A: We know that partition of a set, is a collection of n disjoint subsets, say P1,P2...Pn that…

Q: (aib} oPen set is [arb) ofen? ? closed set Is Is QoPen set

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Q: | If two sets are equivalent, then they are also equal. (True or False?) A is not a subset of B.…

A: These are discussed according to definition in set theory.

Q: State Principle of Inclusion and Exclusion for four sets and prove the statement by only assuming…

A: Let the four sets be A, B, C, D Since, Principle of Inclusion and Exclusion holds for three sets…

Q: A topological space is dis connected if and only if it contain non empty set which is both open and…

A: I give you two simple example with explanation

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: 5. Let S be a set containing 8 elements. What is the number of subsets of S containing at least two…

A: Question 4: A relation ~ on set N of natural numbers. For natural numbers, n and m,  n~m⇔ϕn=ϕm. To…

Q: 6. Let S be a set containing 700 elements. which is greater, the number of subsets of S having 400…

A: We have given as set 'S' with '700' elements in it. Concept:  CARDINALITY -- Cardinality is the…

Q: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: Given

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

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 8. Give an example to show that the arbitrary intersection of open sets is not an open set. 9. Give…

A:

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: (2) Cantors Paradox demonstrates that there is no set of all sets. We know that every set has a…

A: Cantors Paradox states that there is not set of all sets. Proof:  We know that every set has a…

Q: Determine if the union/intersection of two open sets is always open then determine if the…

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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: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: {0,1,3,4,5} is the smallest set that contains {1, 3, 4} and {0, 3, 5} as sub-sets.

Q: True or false 1.The intersection of two sets is the set of all the equal elements that belong to…

A: Since you have not mentioned the questions to be solved, so we are providing you solutions for first…

Q: How

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Q: Please help me with this. Use element argument to prove the statement. Assume that all sets are…

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Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A:

Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

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Q: Let U be the universal set of all the letters in the English alphabet. What is the complement of the…

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Q: Prove that the greatest member of a set, if exits, is the least upper bound of the set,

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Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: A set has 9 elements. How many subsets of S are there with at most 2 elements?

A: Given,            A set has 9 elements. Subsets of S are there with at most 2 elements.

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: 4.3 Give an example to show that the arbitrary intersection of open sets is not an open set.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

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

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Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: Three sets divide the universal set into at most ___ regions.

A: Consider a universal set U with three subsets A, B and C. The Venn diagram for three overlapping…

Q: 8. The set of even numbers less than 100 is infinite. 9. The cardinality of a null set is zero. 10.…

A: 9. Cardinality of any set is the number of distinct elements that set contains. for example- P=A,B,D…

Q: Let U = {3, 4, 5, 6, 7, 8, 9}. List all the members of the given set.  {x | x is less than 7} ∩ {x…

A: The set A ∩ B defines the collection of common units of sets A and B.