2. Enumerate (i.e. list) the members of the following sets: a. {z |z is odd positive integer and z < 13} b. {x |x is an positive integer and x³ < 1000}

Q: Which of the following sets are finite or infinite(i) The set of months of a year(ii) {1, 2, 3, . .…

A:

Q: Identify the following set as finite or infinite. x|x is a rational number smaller than 3} Chooro

A: Given set { x | x is a rational number smaller than 3}

Q: 4. Write out the following sets, and give a formal proof that set-builder notation expression (as…

A: The set builder notation is given as, {x∈ℝ: x2=x} × {x∈ℕ : x2=x} As in the case of real numbers all…

Q: (2) (a) Give an element chasing proof to show that the empty set Ø is a subset of any set A. (b)…

A:

Q: 2. Use the set builder notation to give a description of each of the following sets: 1 2 3 4 5 2'3'…

A: Given

Q: . Is it true that the null set is a subset of every other set? (Y/N)

A: If a set has no element then the set is called null set. Null set is also called empty set. It is…

Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let A…

Q: (1) Prove, or come up with as simple a counterexample as you can: For sets A, B, in the context of a…

A:

Q: True or False If A is a set, the complement of A is the setof all the elements in the universal set…

A: Complement of a set A: Consider a set A. Then the complement of the set A is the set of all elements…

Q: consider the following sets, with U = N; that is, the universal set is the set of natural numbers: A…

A: Given that, C = {1, 3, 5, 7, 9, 11, 13, ............... }

Q: Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) A…

A:

Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: Express the following in set-builder notation: (c) The open interval C = (−2, 2). (d) The set D of…

A: (c) C = (-2, 2) = { x ∈ R :  - 2 &lt; x &lt; 2 } (d) D = { A ⊆ N : #(A) = 20 } Where, #(A)…

Q: d. What is the cardinality of a countably infinite set?

A:

Q: For an element to be in the intersection of sets A and B, the element must be in set Am in set B.…

A: Any elements of A intersection B must be in set A and in set B

Q: А - (ВnС) %3D(А — В) n (А — С)

A:

Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

A:

Q: The set of elements that are members of set A or set B or of both sets is called the. of sets A and…

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

A: Given C and D are two subsets of universal set U.

Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: Calculate the number of subsets and the number of proper subsets for the given set. {x|x€N and…

A:

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: 10. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Which of the following sets is a universal set for the other four sets? O The set of even natural…

A: .

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: 4. Let A be an open set in å nörmed space subset B of X .

A: Que  Ans :  Given ( X, ||-||) be a norm linear space,  A be any open subset of X    ( def- set A is…

Q: Let C and D are be the subsets of some universal set U. Then D-C = C'nD is

A: We have to identify the statements as true or false.

Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: b. Define the finite and infinite sets in your own words and give example for each set.

A: We use the definition of finite and infinite set to answer the given question.

Q: Determine n(U), the number of elements in the universal set, given n(X) = 47 and n(X′) = 156.

A: Note : {X, X'} forms a partition of U. i.e. X &amp; X' are disjoint and their union is the universal…

Q: Which of the following is NOT a finite set? * O A set of vowels. O {x:xE N, 1<x < 5} O (x:xe Z} O A…

A:

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

Q: Show that the set of Natural Numbers (N) is a closed set.

A: The objective is to prove that the set of natural numbers is closed. To prove that it is closed we…

Q: Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable…

A:

Q: 20. What is the cardinality of each of these sets? а) и c) {Ø, {Ø}} b) {Ø} d) {Ø, {Ø}, {Ø, {Ø}}}

A:

Q: 6. Find the complement of the following sets if universal set is the set of natural numbers. (a) {x…

A:

Q: Find the cardinal number of the set C={(1/x) ∣ x is an integer that's greater than or equal to 4…

A:

Q: Is A countable or uncountable?

A: This is a problem of real numbers properties of topology.

Q: 1. Use counting to determine the whole number that corresponds to the cardinality of these sets. (a)…

A:

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

A:

Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

A: Given that set A and set B have 6 and 9 respectively. Now that A is a proper subset of B which means…

Q: Determine whether each of the following statements is true or false, and explain why.The number of…

A: Let A and B be two non-empty sets. Number of elements in set A = m Number of elements in set B = n…

Q: Determine whether each of the following statements is true or false, and explain why.A set is a…

A: A set A is subset of another set B if all elements of the set A are elements of the set B.

Q: What is the cardinality of the set of integers X defined below? X={n| 1<n<12 n is not divisible by…

A: Introduction :

Q: Which of the following sets is NOT well-defined?:   -The set of correct answers in the exam. -The…

A:

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is:

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Q: 4. Suppose you wanted ; –) and :0 to be the elements of a set S. (a) How could you indicate this? In…

A: We want ;-) and :o to be the elements of a set S.

Q: let sets a and b be defined as follows. A is the set of integers than or equal -5 and less than or…

A: Solution: Let sets A and B A={the set of integers greater than or equal -5 and less than or equal to…