1) Use any method(descriptive, roster method and set builder notation) to give three examples of sets in real-life that are infinite. 2)Use any method(descriptive, roster method and set builder notation) to give three examples of sets in real-life that are infinite. 3)Use any method(descriptive, roster method and set builder notation) to give three examples of sets in real-life that are empty

Q: What is the set M of positive integers less than 100?

A: Given statement is set consist all those positive integers less then 100. Collection of all these…

Q: If the number of elements in a set is a nonnegative integer,we say that the set is_______

A: Finite sets- A set with finite number of elements is known as finite set. The number of elements in…

Q: 37 How can we use product rule to count number of subsets of a finite set ‘A’?

A: 37 How can we use product rule to count number of subsets of a finite set ‘A’?

Q: Define Open set ?

A:

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

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Q: prove or disprove using any valid method of proof for sets

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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: Provide a counter example that infinity intersection of open set is open

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

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Q: 4. (10 points) Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite…

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Q: What is the other name for the “rule method” in describing a set?  (A) roster (B) defining property…

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Q: 26

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

Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

Q: The family of all finite subsets of a countable sets is countable.

A: Countability

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: Explain what is a finite set. Give relevant example along with.

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Q: Do infinite uncountable sets have the same cardinality? If yes explain why. If no give a counter…

A: No. Infinite uncountable sets may have different cardinality.

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: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: 8. (a) Show that the intersection of finitely many open sets is open.

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

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: Prove: The Cartesian product of countable sets is countable.

A:

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: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

A:

Q: Determine whether the set if finite or infinite The set of  of odd numbers greater than 3.  is is…

A: We need to determine whether the given set is finite or infinite. Let A = the set of odd numbers…

Q: 5. Show that a finite union of countable sets is countable.

A: The answer is given as follows :

Q: Propose a partial order on a non-empty finite set so that it has 3 maximal elements and two minimal…

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Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: Write an example of a partially ordered set which is not totally ordered. Explain the reasons. Are…

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Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

Q: Remark. Every (finite Countable set is negligible or infinite)

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

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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: Every uncountable set in a 2nd countable space has a limit point.

A: We have to prove that every uncountable set in 2nd countable space a limit point. Definition:- Let…

Q: specify the set by roster distinct letters in the word (mathematics)

A: Given that

Q: prove that the union of a countable set and an uncountable set is uncountable

A:

Q: ) Find an example of an infinite collection of closed sets whose union is not closed.

A: Any closed interval is closed in R. From that we created this example.

Q: Show that the set of odd numbers is countable.

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Q: What will be the cartesian product of three sets if one set of them is empty?

A: The answer is given as follows:

Q: Write out an expression for a set (in set notation) that includes all divisible by three and all…

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Q: The defining property of an ordered pair is that two or- dered pairs are equal if and only if their…

A: Firstly suppose that a,b=c,d i.e a,a,b=c,c,d. We have to show that a=c & b=d. There will be two…

Q: which method is best to describe an infinite set?

A: The solution is given below

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: Explain Cantor, of way 2. proving the set of algebraic numbers is countable Set.

A: The set of integers is countable, we have this following theorem: So by this theorem, the set of all…

Q: what are infinite subsets?

A: First understand, what is an infinite set?

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”.