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

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: 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: Select the collection of sets that forms a partitic

A: Introduction: A set of disjoint subsets of another set. The original set must be equal to the sum of…

Q: Prove that the union of countable set is countable

A:

Q: Define Open set ?

A:

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: What is the class width (i) if one of the class interval is 18-26?

A: If class interval given is 18-26 The class width is difference between upper interval and lower…

Q: Assume that there are 3 pairs of black socks (çorap), 1 pair of pink socks, and 2 pairs of blue…

A:

Q: A set has 20 elements. How many subsets of the set can be formed such that each subset consists of…

A:

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: If a set A has 63 proper subsets, what is |A|? *

A: Solution...

Q: of these collections of subsets are partitions of the set of integers? Explain your answer.   The…

A: Given: The set of even integers and the set of odd integers. The set of positive integers and the…

Q: 2. (i) Show that given finitely many countable sets A1, A2, , An, the set A1 x A2 x .. x An is also…

A:

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

A: Countability

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

A:

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: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

A:

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: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

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

A:

Q: subset

A:

Q: The infinite in tersection of -pon Set is ofen set.

A:

Q: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

Q: There is a countable collection of compact sets whose union is not compact. Select one: O True False

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Give an example of a countable collection of bounded sets whose union bounded, and an example where…

A: Let A1 and A2  are bounded sets

Q: Find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10} as subsets.

A:

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

A: The answer is given as follows :

Q: A set with 6 elements has —- subsets

A:

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

A:

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: 3. Find the number of subsets for set containing 3 elements.

A: Given set  containing 3 element

Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set. Correct…

A:

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: 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: Assume that there are 2 pairs of black socks (çorap),3 pair of pink socks, and 5 pairs of blue socks…

A:

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: ) 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: 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: Find the number of subsets of the given set. {x|x is an even counting number between 9 and 19}

A: We will find the number of subsets of the given set.

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: 5. (a) How many functions are there from a set with n elements to a set with m elements?

A:

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

A:

Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

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…