Is the relation of “mapping” between two sets used to determine cardinality - and not used to determine the subset relation? (Y/N)

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: Every equivalence relation is reflexive. True False

A: A relation is said to be an equivalence relation if and only if the relation R is reflexive,…

Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: 6) Define the cardinality definition of addition.

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Q: What is an example of two equivalent sets with the same cardinality BUT DO NOT HAVE a one-to-one…

A: Take A as, 1,2,3 and B as 3,4,5 The cardinality of A and B is 3. Now let's define a function.

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: 3.1 Show that a finite intersection of closed sets is closed.

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Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

Q: Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) A…

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Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

Q: If S is a relation from a non-empty set A to a nonempty set B then

A: Solution :-

Q: 24) 100 people are surveyed, obtaining the following information: -Every respondent who owns a car…

A: Given that the total number of respondents is 100. There are 54 male respondents. The number of male…

Q: Write out in words the description of the set. {x\x € W, x < 9} The set of ---Select--- X, such that…

A: To write out in words the description of the set.

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: Let B be a denumerable set and let A be a non-empty set of unspecified cardinality. If f : A --> B…

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Q: Give an example of a closed set in R ^ 3 with the usual topology that is not compact

A: Given the usual topology on ℝ3. i.e. τusual=U⊆ℝ3: ∀x∈U, ∃∈&gt;0 such that B∈x⊆U

Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: A set of ordered pairs in which each member of the set of first components corresponds to exactly…

A: We fill the blank space as,

Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

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Q: (2) Cantors Paradox demonstrates that there is no set of all sets. We know that every set has a…

A: Cantors Paradox states that there is not set of all sets. Proof:  We know that every set has a…

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

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Q: Using Richard Hammack's book of Elements of Discrete Mathematics chapter 18 in cardinality. Prove…

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Q: 3. ** Let X, Y be finite sets, and f is a function XY. What can you say about the cardinality if X,…

A: 3. Given X, Y are finite sets and f:X→Y is a function   To Comment about cardinality of X and Y if…

Q: Given two sets X and Y, we denote the cardinality of X by |X| and the set of all functions from X to…

A: We are given two sets X and Y. The set of all functions from X to Y is denoted by YX.  Suppose that…

Q: 1), consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)…

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Q: 2. Identify the sufficient condition in each of the following pairs: It is a consumer. It is a…

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Q: 15. We have seen that an infinite set can be put into a one-to-one correspondence with a proper…

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Q: What is the best choice for the cardinality of A X B when A is finite and not empty, and B is…

A: Given:A=Finite and non emptyB=uncountableCardinality:A×B=Product of A is finite and and B is…

Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}.…

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Q: cardinality of A X B

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Q: Prove that every nonempty subset of a well-ordered set is well-ordered.

A: Given problem is :

Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

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Q: 1. List the domain and range for the relation. {(11, –5), (–10, 15), (3, 5), (7,–5)} O Range: {-5,…

A: according to Bartleby guidelines I am expected to solve only the first question. Kindly repost the…

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: 3.3: Is brotherOf an equivalence relation on the set of all people?? How about siblingof?, same…

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Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

Q: Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection…

A: Yes, the sets 0,1 and 0,12∪12,1 have the same cardinality.

Q: Any two closed intervals has the different cardinality

A: we know that any two closed intervals has the same cardinality

Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: ave a class boundary that is less than zero?  On the probelem I am working, the class goes from 0-5

A: Class boundaries are the values which help in separating the data points in statistics.

Q: 8. The set of even numbers less than 100 is infinite. 9. The cardinality of a null set is zero. 10.…

A: 9. Cardinality of any set is the number of distinct elements that set contains. for example- P=A,B,D…

Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below