Let A={0,1,4,8,10}A={0,1,4,8,10} ,   B={1,4,5,10}B={1,4,5,10}. Find the following sets in list form. Separate elements with commas. If there are no elements in the set, enter "NONE". a) A ∩ B= b) A ∪ B=

Q: Let ? = {1, 2} and ? = {1, 2, 3}. List all the elements in the set (? × ?) ∩ (? × ?)

A: A = {1,2} and, B = {1,2,3} So, A×B = {(1,1,), (1,2), (1,3), (2,1), (2,2), (2,3)} &, B×A =…

Q: If a set A has 63 proper subsets, what is |Al? 6. 7 8. 9

A:

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

A: Example of such set A,B,C,D are given below

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

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

A:

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: Show that for all sets A, B and C, If A CB, then B CA.

A:

Q: Show by membership that for all sets A, B and C: A-(ANB) CA-B

A: Sets and relations

Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: Set C is a set of states in the United States whose names start with the letter H in roster form

A: In this question we have to write a set C in roster form which contains states of United Stated…

Q: If p and q are subsets of the universal set Z, draw a Venn diagram and shade the region representing…

A: Given that, If p and q are subsets of the universal set Z, draw a Venn diagram and shade the region…

Q: Draw a Venn diagram to show the set  An(B U C')

A: Furst find B U C' then An(B U C').

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: 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: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

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: The number of subsets of size r that can be formed from a set with n elements is denoted: O (?) O…

A:

Q: Let A be the set of students in your math class, and B is the set of students at Indiana State…

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: Show that if A, B, and C are sets, then A n Bn C = A U BUC a) by showing each side is a subset of…

A:

Q: Construct a Venn diagram illustrating the sets below. U={a, b, c, d, e, f, g, h} W={a, c, d,f} х-…

A:

Q: Show that for all sets A, B, and C, if A C BUC, then ANC + Ø or A C B.

A: In order to prove this we need to use the property that if X⊂(Y∪Z) ⇔X⊂Y or X⊂Z

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: 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: Show by membership that for all sets A, B and C: А - (AnB) CА - В

A:

Q: Use the Venn diagram below to list the elements of the set A' in roster form. 12 AD 11 (13) 15 14…

A: The Venn diagram is   To determine: The elements of set A in roster form.

Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: Let X= {p, q, r, 15, 16, 17}, Y ={q, s, t, 15, 17, 19}, and Z= {q, s, 16, 17, 19}. List the members…

A: let X={p,q,r,15,16,17}   Y={q,s,t,15,17,19} Z={q,s,16,17,19} find member of X∪(Y∩Z)=?D

Q: Use the Venn diagram below to determine if (AnC) n B= (An B)nC and, if it is, what regions does the…

A: The given Venn diagram is: From the Venn diagram, it is clear that, The elements in set A are as…

Q: Use the Venn diagram pictured with A representing the people in an arts class and B representing the…

A: Solve the given

Q: If A is the a set of symbols representing only and all the vowels used in English, and B is a set of…

A: Set A of vowels = {a,e,i,o,u} Set B of nasal consonants = {m,n} A nasal consonant is a consonant…

Q: Draw the Hasse diagram of the given set of A = ({3, 4, 12, 24, 48, 72},/)

A:

Q: If A={People who have a tattoo} B={People who have a job}, Draw a Venn diagram relating the two…

A: Given: Set A={People who have a tattoo} Set B={People who have a job} Set U={Human beings}

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; wheren is total number of distinct…

A: Consider two sets A and B. Then the union of these two sets contain all the elements in both A and…

Q: Show by membership that for all sets A, B and C A - (AnB) CA-B

A:

Q: Construct a Venn Diagram illustrating the given sets. A = {4,5,6,8}. B= {!,2,4,5, 6,7}, C={3,4,73…

A:

Q: Refer to the Venn diagram below. How many elements are in the set AUB? nAUB) -

A: Given,

Q: The Venn diagram shows sets A, B, C, and the universal set U. Shade (BOC)' UA on the Venn diagram. U…

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…

A: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

A:

Q: The Venn diagram shows sets A, B, C, and the universal set U.

A: Given Venn diagram:

Q: Complete the membership table to show that for all sets A, B: B = (ĀU B) – B A B 11 1 0 0 1

A:

Q: Given a set A of n elements, in how many ways can you find two set P,Q ⊆ A (not necessarily…

A: Given set of  elements we need to find number ways in which A can be written as union of two…

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

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

Q: Is {A, B, C} a subset of the set of letters of the alphabet?

A: Subset is a set of which all elements are containd in another set.

Q: Use the Venn diagram below showing the number of elements in regions I through IV to determine the…

A: The venn diagram showing the number of elements in regions I through IV.we have to find number of…

Q: Express the following set in set builder notation.  B={15,16,17,18,19,20,21,22}

A:

Q: Let the Universal Set, S, have 142 elements. A and B are subsets of S. Set A contains 61 elements…

A: Universal set, S contains 142 elements.Set A contains 61 elementsSet B contains 92 elementsSets A…

Q: Show by membership that for all sets A, B and C: A - (AnB) CA – B

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”.