You just bought a new car from a dealership that sells cars no older than 2015. Consider therelationship to be the “same age.” The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and 2020. (a) Prove that this relation is an equivalence relation. (b) Describe the partition defined by the equivalence classes

Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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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: Given a set define a relation induced by a partition of set A and that partition must consists of at…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

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Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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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: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: (a) A relation is an equivalence relation if it is, reflexive, transitive, and symmetric. Let D be…

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the…

A: Given:-               A car dealership sells cars that were made in 2015 through 2020. Let the cars…

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: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

A:

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

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Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: let R be an equivalence relation and let [x] be the equivalence class of x, prove x belong to [x]

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Q: For every nonempty set A, there exists a relation R which is both an equivalence relation and a…

A: A relation R is said to be equivalence relation if R is Reflexive ,Symmetric and Transitive . R is…

Q: 3. Prove or disprove each of the following properties for the relation below: reflexive, symmetric,…

A: The given relation, which is defined on the set of integers, is…

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A: We have to decide whether given relation is partial order or not?

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

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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: 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: Find the number of different partions of a set (a) with one element (b) with two elements (c)…

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

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Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…

A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: equivalence

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Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is…

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Q: What is the possible number of reflexive relations on a set of 5 elements?

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Q: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…

Q: Define equivalence class and partition of a relation.

A: Define equivalence class and partition of a relation.