Suppose A is a set having n elements. a. How many relations are there on 4? b. How many reflexive relations are there on 4? c. How many symmetric relations are there on A? d. How many relations are there on A that are both reflexive and symmetric?

Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

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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\…

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

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Q: State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram…

A: The formula for The principle of inclusion and exclusion  for three sets A |A\cup B \cup C| = |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: 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: 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: Write the following set in roster form: A={x:x is any two elements that belong to natural number…

A: Just observe step by step, we'll see a pattern.

Q: Let *' be defined on the set N. Which of the following are both commutative and associative?

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Q: 5. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it…

A: Truth table for the symmetric difference is,

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: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

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Q: . How many relations are there on the set S = {2, 4, 6}? 892 512 none of these 1024

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Q: If a set A has 9 elements, then the total number of possible relations on A is O 202 299 O 29 92

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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…

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Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

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Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

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

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Q: Suppose A is a set with n elements and B is a set with m elements. (a) How many ordered pairs (a, b)…

A: By bartelby guidelines I can only answer the first three sub questions.

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 and R is a reflexive and transitive relation on A. Show that the

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

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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: 19. If A={People who live in Colorado} B={People who live in Denver}, draw a Venn diagram relating…

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Q: Suppose that A represents the set of all cucumberand B represents the set of all vegetables. What is…

A: Solution-: We consider, A - represents the set of all cucumber and B- represents the set of all…

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…

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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: Let the universal set be the 26 letters in the English alphabet, and let A = {a, b, c, d}, B={c, d,…

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Q: When using Venn diagrams to verify or determine whether set statements are equal we use…

A: Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements…

Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

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Q: Let S(a, b) = {na + mb : n, m ∈ Z}. For any a and b in Z, not both zero, the set S(a,b) is precisely…

A: Take the set S={ax+by>0:x,y∈Z} Without loss of generality, assume that a<b. Then b−a>0 is…

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: Given the sets ((A n D)U (Bn C)) and (((An D) U B)nc): 4. Determine which one is a subset of the…

A: Given two sets  A∩D∪B∩C and A∩D∪B∩C Note: We will use the following definitions of union and…

Q: 6. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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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: If a set A has 6 elements, then the total number of possible relations on A is 262 260 62 26

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Q: Draw a venn diagram to represent the set A insersects B, but B has a line over it showing its a…

A: To represent the given combination of sets (A intersection B complement) in a Venn diagram

Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

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: Express the following statement into a Set Builder Notation 1. (2, 4, 6, 8, 10} = %3D 2) {2, 3, 5,…

A: Set builder notation consists of { Type of element | Rule defined} Hence 1) {2,4,6,8,10} {x | 2≤x≤10…

Q: (c) Show that the set {r EN | x² % 4 = 1} is equal to the set {EN | x² % 8 = 1}.

A: Two sets are said to be equal if the number of elements in both the sets are equal. Now, we have one…

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…

Q: Let at AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9} and let the universal set U be all positive integer…

A: From the information, AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9}, U={all positive integer less than or…