Suppose S is a set having n elements and T is a set having m elements. Which of the following claim is true? a) The set difference between S and T has n - m elements.  b) The union of S and T has n+m elements. c) The intersection of S and T has at least m elements. d) The intersection of S and T has at most n + m elements.

Q: 2. Find sets A, B, C, D such that the sets (AN B)U (C\ D), ((An B) U C) \ D, An(BUC) \ D, An(BU(C\…

A:

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

A:

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

A:

Q: Use the definition of oubset to prove : If A,B,C are set then ((BnA) -c) U ((Bnc) -A)) CCOUA)

A:

Q: 1. Draw a Venn diagram showing the following: (a) Two sets A, B, where every element of B is an…

A:

Q: Here is some more practice on calculating the number of elements in a set. 10. Suppose A and B are…

A: Given ,           AC U          BC U          nA=73         nB=56        nU=150To find → nA' &…

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

Q: A group of high school students reports who has a job and who plays sports. The information is…

A: lets the event having a job = J event that random person is in sports  = S probability of having 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: Given that set A has 41 elements and set B has 22 elements, determine each of the following. (a) The…

A: Set A : 41 elements  Set B : 22 elements

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where B =…

A:

Q: A survey of 500 farmers showed that of the​ farmers, 26 grew only​ wheat, 114 grew only​ corn, 93…

A: The following situation can be represented by venn diagram given below: Rectangle(universal set)…

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

A:

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

A:

Q: Create a Venn diagram that shows the following elements: • a, b,c, d in set A • x, y, z in set B •…

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

Q: Use the following information to answer question 6. 16 19 The number of elements in the unversal set…

A:

Q: A universal set U with 117 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A:

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

A:

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

Q: Suppose A is a set with 6 elements. Answer the following questions:   1. How many subsets of…

A: In a set the order does not matter. So we can use the combination method. 1) We can pick 4 elements…

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

A:

Q: Use a membership table to determine if AUBUC = Ã U BU Č, when A, B, and C are sets.

A: The given relation is A∪B∪C=A∪B∪C

Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

A: Given: m and n are the positive integers. Set A contains m elements and set B contains n elements.…

Q: Consider the sets A = {x € Z*, x < 13 | x prime} B = {x e Z*,x < 13 | x even} C = {x € Z*,x < 13 |…

A: We know that the set of positive integers is written as . We have to find the size of the set  .…

Q: If S and T are two sets such that S has 21 elements, T has 32 elements, and   S ∩ T has 11 elements,…

A:

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

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: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where…

A:

Q: For all sets A, B, and C, if A C B and BnC = 0 then An C = 0. Construct a proof for the statement by…

A:

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

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

Q: Consider the sets A = {x € Z*,x < 13 | x prime} B = {x € Z*, x < 13 | x even} C = {x € Z*,x < 13 |…

A: For three sets A, B, and C it can be said that, A ∪ B ∪ C implies the set of elements that belong to…

Q: 2. Use the element method of proof to prove that for all sets A, B, and C, (An B) -CCANC.

A:

Q: Given set A with 17 elements and set B with 7 elements. a. What is the maximum number of elements in…

A: Given set A with 17 elements and set B with 7 elements. If all the elements of set A and set B are…

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Use a Venn diagram to determine if the pair of sets are equal. S. S'nT and (SUT')' II III IV

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

Q: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

A:

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

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: O AC Biff P(A) C P(B).

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

Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

A: Given that,                     m and n are positive integers.                    A is a set with…

Q: 2. Draw a Venn diagram for the set AU(BnC).

A: We first draw U, A, B, C

Q: Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly…

A: Given, A is a set with 7 elements In a set the order doesnot matter so here we use combinations.

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: Let A=​{peach, kiwi, tomato, raisin​}, B=​{lemon, watermelon​}, and C {tomato, lemon, pear,…

A: Let A and B be two sets .         1.)  n( A∪B)=nA+n(B)-n(A∩B)         2.) n(A∪B)= n(A-B)+n(A∩B)+ n…

Q: In drawing 3 CD’s from a lot, defective and non defective CD’s , let A, B , C and D mean at least…

A: let A, B , C and D mean at least one Defective CD, at least one non defective CD, 2 defective CD’s…

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.

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”.