The set {{8}, {9, 10}, {11}} is a partition of the set A. Define the equivalence relation R on the set A whose equivalence classes are given in the partition by listing all ordered pairs in the relation.

Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

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

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

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: Prove that the relation of congruence is an equivalence relation.

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

Q: Let A = {82,95, 146, 153, 158, 166, 180, 187, 207} and R be an equivalence relation defined on A…

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Q: Given the sets A = {a, b, c, d}, B = {0, 1, 2, 3} construct a relation R such that R is an injective…

A: There are two question , one is related to relation and function , second is related to equivalence…

Q: Let Z be the set of integers. Z = (- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation…

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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: Let A be a set and R be a symmetric and transitive relation on A. Prove the following statement: If…

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

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: Let R={ (a,a). (a,b). (b.b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e). (d.f).…

A: Given:  R = (a, a), (a, b), (b, b), (b, a), (c, c), (d, d), (e, e), (f, f), (d, e), (e, d), (e, f),…

Q: Given any fixed integer n. Defined the relation on Z, a ~ b if and only if a - b is divisible by n.…

A: This is a relation and functions problem

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Show that the relation R in the set A of all the books in a library of a college,given by R = {(x,…

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Q: for an equivalence relation R on A, both sets, the class of equivalence classes of R —A/R— is a set.

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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: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

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.

Q: Let Z be the set of integers. Z = {- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation…

A: I just used the definition of equivalence classes

Q: Let H be the set of all human beings. Consider the relation R defined on H by xRy if and only if x…

A: R defined on H by xRy if and only if x and y have the same biological mother. reflexivity : x &…

Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are…

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Q: (a) Show that R is an equivalence relation. (b) List three members of each of the equivalence…

A: Equivalence relation: A relation R is called an equivalence relation in a set A, if it follows the…

Q: Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove…

A: A relation R on a set A is said to be an equivalence relation, if it satisfies the following three…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Let A be a set and let ∼ be an equivalence relation on A. Let x, y ∈ A. Prove that [x] = [y] if and…

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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: Question No. 5) Show that a partition of a set S determined equivalence Relation on set S. (

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

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

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

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Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example   9R10,10R11⇒9R  11

Q: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: There are as many equivalence classes as there are which of the following? (Select all that apply.)

A: There are many equivalence classes.

Q: Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and…

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Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

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

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Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…

A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Let R be the relation on the set of all people who have visited a particular Web page such that x Ry…

A: Given

Q: equivalence

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Q: Define equivalence class and partition of a relation.

A: Define equivalence class and partition of a relation.