7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 = xx4. List the elements of the equivalence class [(2,2)].

Q: 9.32. A relation Ris defined on the set A = {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show…

A:

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1, 2} defined by (a, b)S(c, d) if and…

A: S=0,1,2,3×0,1,2=0,0;0,1;0,21.0;1,1;1,22.0;2,1;2,23.0;3,1;3,2

Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

A:

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

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

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

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: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

A:

Q: Let R be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and…

A: Let R be a relation on a set A R is an equivalence relation if it is reflexive, symmetric,…

Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

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: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

A:

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: PROBLEM 30. For (x, y) and (u, v) in R2, define (x, y) ~ (u, v) if x² + y² = u? + v?. Prove that…

A:

Q: Let A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

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Q: 2. Define the relation on S = Z by a~b + a = b mod 5. (1) Prove that is an equivalence relation. (2)…

A:

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: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

A:

Q: 5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if…

A:

Q: True or False? Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then…

A:

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

A:

Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

A:

Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

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: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

A:

Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

A:

Q: Let ~ be defined on the set X = {0,1,2,3,4,5,6,7,8,9} by x ~ y + x2 = y? mod 5. Prove that is an…

A: Equivalence relation are those which are reflexive symmetric and transitive

Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

A:

Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

A:

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

A:

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

A:

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

A:

Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

A:

Q: Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalence relation on S. R =…

A: Given relation R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)} on  S =…

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

A:

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: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information:

Q: Prove that the following relation is equivalence relations and prepare it in latex: On R, with x∼y…

A: Revision : A relation ~ defined on a set  A is an equivalence relation if and only if it satisfies…

Q: 14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an…

A:

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: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

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: 40

A: By using the definition of equivalence relation solution is given as follows :

Q: 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

A: