My NotesAsk Your Teacher   Let A and B be subsets of a universal set U and suppose n(U) = 360, n(A) = 125, n(B) = 90, and n(A ∩ B) = 50. Find the number of elements in the set. n(Ac ∩ Bc)  elements

Q: 9. What is the set-builder equivalent of {0, 1, 2 }? 10. What is the set-roster equivalent of {x E…

A: Set: Set is any collection of objects or elements which may be numerical or non-numerical. Set…

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 of the following sets are closed under addition? Explain why they are or are not closed. d.…

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Which of the following is the correct representation of A {2,4,8,16,32,... } in set builder…

A: To determine the correct representation of A=2, 4, 8, 16, 32, ... in set builder notation.

Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(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: 1. Define three different sets using roster notation; refer to them as sets A, B, and C…

A:

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

A:

Q: a) Suppose A, B and C are sets. What do you need to show to prove the following using the definition…

A: Definition : A⊂B iff (x∈A⇒x∈B)WLOG : Without Loss Of Generality.

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: 1. a) Suppose A, B and C are sets. What do you need to show to prove the following using the…

A:

Q: Let the Universal Set, S, have 89 elements. A and B are subsets of S. Set A contains 37 elements and…

A: Given that :  S have 89 elements A have 37 elements B have 30 elements A and B have 25 elements in…

Q: 6. Suppose that U is an infinite universal set, and A and B are infinite subsets of U. Answer the…

A:

Q: c) Create a set comprehension for the set F = {1,2,4,8 %3D

A: Solution of the problem as follows

Q: 10. Using the figure on the right and U = {a, b, c, d, e, ƒ ,g,h} being the universal set, find the…

A: We can find the answer as below using the rules of set theory.

Q: Let U be a universal set with disjoint subsets A and B such that n(A)=44, n(A′)=45, and n(B′)=70.…

A: Given data: The number of elements in A is n(A)=44. The number of elements not in A is n(A')=45. The…

Q: Determine if the following statements are true or false. Here A represents any set. (a) oCA (b) A'CA…

A: Here let us consider A to be any set which consists some elements U is a universal set  A' is a…

Q: 4. Let the universal set U, and the subsets of U are A = {x\x is a letter of your first name}, (R my…

A:

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: Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B…

A: Consider the given sets:

Q: 4. Let the universal set U, and the subsets of U are A = {x\x is a letter of your first name}, B =…

A: Let us solve the set problems and describe various types of sets in the next steps.

Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: 2. Let C and D be subsets of a universal set U, then 2, (C ∩ D) ⊆ (C4D).

A: False

Q: Suppose S is a set having n elements and T is a set having m elements. Which of the following claim…

A: Suppose S is set having n elements and T is a set having m elements. That is n>m More precisely,…

Q: If H={1,2,3} and P={2,3,5}. How many proper subsets does H∩P have? (Don’t forget the empty set!)

A: If the cardinality of a set is n then a number of subsets of S will be 2n - 1.

Q: Let the Universal Set, S, have 141 elements. A and B are subsets of S. Set A contains 96 elements…

A: Universal set S contains 141 elements. Set A contains 96 elements. Set B contains 57 elements. Total…

Q: Let A = {a,b,c,d,e}, B = {a,b,c,d,e,f,g,h}, and U represents a Universal Set of…

A:

Q: 4. Let the universal set U, and the subsets of U are A = {x|x is a letter of your first name}, B =…

A: Disclamier: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: Match the following term with the appropriate description​ A-F below. Assume A and B are sets.   The…

A:

Q: 4. Let the universal set U, and the subsets of U are A = {x\x is a letter of your first name}, (R my…

A: (a) To write: The universal set U. Calculation: The element of set A can be obtained as, A=R The set…

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Please prove the statement below: For all sets X, Y, and Z subsets of a universal set U (X -- Y) ∩…

A:

Q: Let the Universal Set, S, have 101 elements. A and B are subsets of S. Set A contains 59 elements…

A: It is given that,  set A contain 59 elements, n(A) =59 Set B contain 38 elements, n(B) =38 Set A and…

Q: IV. Using the Rule Method and the Set builder notation to describe each of the following sets whose…

A: 1. The given set is D=Rudy, crocodile, π. Then by rule method it can be written as D=x| x is a name.…

Q: Exercise 1.5.5. (a) Why is A- A for every set A? (b) Given sets A and B, explain why A~ B is…

A: (a) To prove that, A ~ A for every set A.

Q: Let the Universal Set be S. Let A and B are subsets of S. Set A contains 29 elements and Set B…

A: Introduction: A universal set is a set containing all the element. No element is repeated in the…

Q: 4. Let the universal set U, and the subsets of U are A = {x\x is a letter of your first name}, (R my…

A:

Q: point the step in the argument that is not valid and explain why ? Theorum: For all sets A,B   A’∪B’…

A:

Q: The union of the universal set and any of its subset is * none of the choices cannot be determined…

A: our objective is to conclude

Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: We have to show that given relations is False.

Q: rea

A: Let A be set of having n elements, then the total number of subsets of A is 2n. Out of n elements ,…

Q: Show that the set EE is: (ii). Closed iff E¯=E

A: Show that the set E is Closed iff E¯=E

Q: Determine whether the following pair of sets is equivalent. Justify your answer. {a, b, c, d,.., z}…

A: Given the two set  {a , b, c ,d ,........, z } and  {1 ,2 ,3 , 4 ,........ ,26} We need to check…

Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A:

Q: Which of the following is the correct representation of A = (2,4.8.16.32. in set builder notation? A…

A:

Q: ets kercises 1.1 Let U = {x : x is a distinct letter of the word mathematics}, А 3D {m, а, t, h}, В…

A:

Q: 2 3 a. Write the set in the set-builder form. b. Write the following set in roster form: A={x:x is…

A:

Q: 1) A) What is a subset of a set? B) Why is {3,6,15} not a subset of {2,15,3,10}?

A:

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”.