Determine if each set countable or uncountable. Show a proof or argument to justify your decision for each set. a) Real numbers between and including 2 and 4, i.e., the set [2, 4] b) Integers between and including 1 and 100, i.e., the set {1, 2, 3, ., 100} c) Integers greater then equal to 2, i.e., the set {2, 3, 4, .}

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

A:

Q: Let the Universal Set, S, have 146 elements. A and B are subsets of S. Set A contains 84 elements…

A: Given that universal Set  S have 146 elements. Set A contains 84 elements. Set B contains 25…

Q: Which sets are compact? The set of natural numbers less than some number M

A: We know that a set is compact if and only if it is closed and bounded. The set of natural numbers…

Q: 15. Identify the type of set (Finite, Infinite, Empty): a. "The Intersection of Even Numbers and…

A: Dear student,                     According to our guidelines we are supposed to answer only first…

Q: Suppose the universal set is the set of natural numbers N. Consider the sets A = {1,2, 3, 4, 5, 6}…

A: We will answer the first three questions as per our guideline. Please resubmit the other questions…

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

A:

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Determine whether each set of mea acute, obtuse, or right. Justify your 1. 30, 40, 50

A:

Q: 3. Let A and B be two sets. Use set operation properties to prove the identity ,AÐB = AUBU (AO B).

A: To prove the identity

Q: Consider the set of whole numbers from 1 to 10, inclusive. List the numbers that meet the condition:…

A: Given set is {1,2,3,4,5,6,7,8,9,10}

Q: Complete the proof using only set identities and definitions. Suppose A, B, and C are any sets. Then…

A:

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

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: А - (ВnС) %3D(А — В) n (А — С)

A:

Q: Let the Universal Set, S, have 146 elements. A and B are subsets of S. Set A contains 84 elements…

A: Provided information is , n(S)=146 n(A)=84 n(B)=25 n(A or B)=n(A U B)=103 Definition of B∩ Ac: It…

Q: Let the Universal Set, S, have 113 elements. A and B are subsets of S. Set A contains 77 elements…

A: From the provided information, n(U) = 113, n(A) = 77, n(B) = 17 And n (A Ո B) = 13

Q: Using the fact that "a countable union of countable sets is countable", show that the statement that…

A: Please see the below picture for detailed solution.

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

A:

Q: 4) Using equality of sets, prove that (An B)' = A' U B'

A: we know thatA∪B=x: x∈A or x∈BA∩B=x: x∈A or x∈BA'=x:x∈U, x∉A=U \ AWhere U is a universal set.That is…

Q: Describe a set in terms of A and B (using set notation) which has the following Venn diagram. (image…

A: the set notation for the given diagram is given below:

Q: Let the universal set be E={whole numbers less than 20}and let A={squares less than 20} B={even…

A: Given sets are  E=Whole numbers less than 20=x∈ℤ:0≤x&lt;20A=Squares less than 20=1,4,9,16B=Even…

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: Let the Universal Set, S, have 114 elements. A and B are subsets of S. Set A contains 31 elements…

A: Universal set, S have 114 elementsset A contains 31 elementsset B contains 63 elementssets A and B…

Q: Assume that A = {1, 2, 3, 5, 8, 7} B = {5, 3, 4} C = {2, 3, 5, 6} and that U is the universal set of…

A: It is basic set theory problem

Q: Assume all sets are subsets of a universal set U. Suppose that A, B, and C are arbitrary sets, Prove…

A: Given, A-C∪B-C=A-Bc∪C

Q: Let A = {3, 9, 1, 8, 2, 6} B = {5, 9, 8, 7} and U be the universal set of natural numbers less than…

A: Explanation of the solution is given below...

Q: Let the Universal Set, S, have 135 elements. A and B are subsets of S. Set A contains 93 elements…

A:

Q: Which of the following sets is NOT an empty set? Select one: a. The set of natural numbers less than…

A:

Q: • Assume all sets are subsets of a universal set U. Suppose that A, B, and C are arbitrary sets,…

A: For problem a i have proved the both seth inequality. And for second i have used algebraic method

Q: Given a universal set containing integers from 0 to 21. Set B contains odd numbers while set A…

A: Given: Given a universal set containing integers from 0 to 21. Set B contains odd numbers while set…

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: Use element argument method to prove that if A and B are sets such that P(A) ≤ P(B), then A ≤ B,…

A: I just used the definition  Of power set and subset of set

Q: Is the set named empty, finite, or infinite? {points on a line} {baseballs used in a major league…

A: A set is empty if there is no element in it. A set is finite if there are countable elements in it.…

Q: Let the Universal Set, S, have 139 elements. A and B are subsets of S. Set A contains 69 elements…

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: state which of the following sets is finite or null (empty) a) the set of persons who have…

A: By the definition  we know, A finite set is one which has a definite number of elements.  An…

Q: Suppose that the universal set U is the set defined as U={1,2,3,4,5,6,7,8,9,10} Write the sets A…

A:

Q: Consider the following statement. (Assume that all sets are subsets of a universal set U.) For all…

A:

Q: Let the universal set U = {x | x is a non-negative integer}. Let A = {r €U | z is divisible by 6}, B…

A: This is a problem of sets. Based on given condition we will generate all the sets along with…

Q: Which sets are compact? The set of integers L

A: The objective is to determine whether the set of integers ℤ is compact or not.

Q: Determine all numbers n belong to N with the property that the set: A = {n, n + 1, n + 2, n + 3, n +…

A: SOLUTION:

Q: Let the Universal Set, S, have 190 elements. A and B are subsets of S. Set A contains 95 element and…

A: Given Information: Universal set S has 190 elements. Set A contains 95 elements. Set B contains 78…

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: Which of the following sets are finite and which are infinite ? (i) Set of lines which are parallel…

A: We know that ,  A set is collection of any objects. Finite sets are the sets having  a finite or…

Q: Write the set in set-builder notation. {3, 4, 5, 6, 7} {x | x =         ,  where n is an integer…

A:

Q: 5. Use element proof to show that for any sets A and B, if A ≤ B then A U B = B. 6. Construct an…

A:

Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

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: In the Venn diagram, the universal set, S, represents all positive integers less than 10. O 2020…

A: if A is a universal set and B is any subset of A then complement of B denoted as  Bc is defined as…

Q: Identify each set as finite or infinite. Then determine whether 10 is an elementof the set. \{x \mid…

A: The given set is, natural number between 9 and 11