Determine whether each relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. (a) The domain is a group of people. Person z is related to person y under relation M if z and y have the same favorite color. You can assume that there is at least one pair in the group, z and y, such that zMy.

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…

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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: 5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}. Define a relation R on S as follows:…

A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: Let A = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows: For all m, n…

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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: A playground consists of several structures, some of which are connected by bridges. The ground is…

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Q: = {1,2,3,4,5} and define a relation R on S x S by (a, b)R(c,d) if ad = bc. Show that R is an…

A:

Q: 4. Let A = (a, b,c, d). Suppose R is an equivalence relation on A. Suppose R has three equivalence…

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

Q: Let A = {-5, –4, –3, -2, –1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n E A,…

A: Given that 5|(m2-n2) is a equivalence relation.  Where m,n∈A and A=-5,-4,-3,-2,-1,0,1,2,3 The…

Q: Let A = {-5,-4,-3,-2,-1,0,1,2,3} and define a relation R on A as follows: For all m, n ∈ A, m R n…

A: We know that For a given set A  and an equivalence relation R on A, the equivalence class of an…

Q: Let A = {a, b, c, d} and define a relation R on A as follows: R = {(a, a), (b, b), (b, d), (c, c),…

A: Equivalence classes of  [a]={a}.   Since only the element "a" is in the relation with "a" .…

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: Let A = {1, 2, 3, 4, ..., 23} and define a relation R on A as follows: For all x, y € A, x R y =…

A: Solution is in next step

Q: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² > 0 But, for n = 0…

Q: 4. Let A = {a, b, c, d}. Suppose R is an equivalence relation on A. Suppose R has three equivalence…

A: To Determine: write R as a set .describe then all   Given: let A={a,b,c,d} suppose R is an…

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

A:

Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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: Let A = {-3, -2, -1, 0, 1, 2, 3, 4, 5} and define a relation R on A as follows: For all m, n E A, m…

A: The given set A is -3,-2,-1,0,1,2,3,4,5 and relation is defined on A is  For all m,n∈A, m R…

Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

A:

Q: an equivalence relation c

A: (a) Given, the function                                      id : X→ X     defined by…

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: According to the given information it is required to check whether the given relation in each part…

Q: Let A = {-7, -6, –5, -4, –3, -2, –1, 0, 1, 2, 3} and define a relation R on A as follows: For all m,…

A:

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m   ∀m∈ℚ…

Q: Let A = {a, b, c, d} and define a relation R on A as follows: R%3D {(а, a), (b, Б), (ь, d), (с, с),…

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Q: Let A = {1, 2, 3, 4, ..., 19} and define a relation R on A as follows: For all x, y E A, x R y +…

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Q: equivalence relation

A:

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A:

Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: a) Consider the given relation M. To prove M is an equivalence relation. For that, M must be…

Q: ) The domain is a group of people. Person x is related to person y under relation S if x is…

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Q: Determine if the relation described is an equivalence relation on the given set. Let S = Z+, a ~ b…

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Q: Let - be a relation on a set X defined as below. Determine whether is an equivalence relation on X…

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Q: Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if…

A: Let A be a non empty set, A relation R on A is said to be an equivalent relation if  1) R is…

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

A:

Q: Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a…

A:

Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

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

A: Given that, The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and…

Q: Let A = {a, b, c, d} and define a relation R on A as follows: R = {(a, a), (b, b), (b, d), (c, c),…

A: When the elements of some set S have a notion of equivalence defined on them, then one may naturally…

Q: Q5: Given a set A of all people in your 230 class, consider a binary relation R between a pair of…

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Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: (b) Given that the domain is the set of all integers. The relation E is defined as follows. For x, y…

Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: a ∼ b in R if a ≤ b

A: To check whether the relation R is equivalence or not: a≤b CHECK REFLEXIVE If the relation is…