Let A = {1,2,3,4,5} B= (6,7,8,9} Define an equivalence relation of p in A UB with atleast 12 members

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: 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".…

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Q: Let R be a relation on the set N of positive integers defined by aRb if and only if the product axb…

A: This question is about equivalence  class .

Q: Define a binary relation R on the set A = {binary strings of length 6} as follows: For all strings…

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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: 1. Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible…

A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…

Q: Prove the understated statements concerning the relation < on the set Z of all integers . If    x…

A: x = y  and     O < z

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: Need help trying to solve this

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

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: 3. Let R be the relation defined on Z by aRb if and only if 5 | (4a + b). Prove that R is an…

A: We have given relation on ℤ and defined by  aRb if and only if 5|(4a+b). We can  see here for any…

Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

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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: 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: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

Q: Consider the equivalence relation ~ on R given by a ~ b if and only if [a] = [b]. You do not need to…

A: Given that the equivalence relation ~ on ℝ defined as a~b if and only if a=b. Define a function…

Q: Let A be the set A-(1, 2, 3} The binary relation R={(1,2), (2,1), (1,3), (3,1), (1,1), (3,3) }…

A: Given: A = 1, 2, 3 and R = (1, 2), (2, 1), (1, 3), (3, 1), (1, 1), (3, 3).

Q: Let D be the binary relation defined below. For all u, w e 2, u D w → w=u +7 or w= u - 7. Show…

A: Solution of given problem is as below: A binary relation is equivalance relation if it satisfies the…

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

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 R be an equivalence relation on A = {3, 4, 6, 7,8, 9} and R = {(8,3), (3, 8), (8, 8), (3, 3),…

A: Equivalence class: Consider an equivalence relation R on a set A. The equivalence class of an…

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

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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…

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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: 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: 6. Consider the partition P = {{0}, {-1,1}, {-2,2}, {-3,3},{-4,4},...} of Z. Describe the…

A: Given the partition of Z is P=0,-1,1,-2,2,-3,3,-4,4,....

Q: Let RR be a binary relation on A={a,b,c}A={a,b,c} given by…

A: We check relationship is reflexive or not

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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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: 1. Show that R is an equivalence relation on P(A). 2. Set A = {1, 2, 3, 4} and B = {1, 24}.…

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Q: Let A={1,2,3,4,5,6} and let R be the equivalence relation on A defined by…

A: Two elements are in same equivalence class if they have an equivalence relation. Given :…

Q: . The relation R on Z defined by a Rb if a? = b² (mod 4) is known to be an equivalence relation.…

A: Consider the given information.

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

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

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Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

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Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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Q: Let A = {55, 63, 70, 83, 86, 106, 113, 116, 151} and R be an equivalence relation defined on A where…

A: Given : A=55, 63, 70, 83, 86, 106, 113, 116, 151 and R is an equivalence relation defined on A where…

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…

Q: (5) Let A={-2,-1,0,1,2}. R is an equivalence relation defined as: for all x,y E A, xRy 2| (x-y?).…

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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: Consider the set A = {2, 3, 5, 7}. Create a relation R on A that is a partial order with at least…

A: The given set is  A=2,3,5,7 and we have to define a partial order relation R on set A with at least…

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…

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

Q: Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1),…

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

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Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (3,1), (3,2)} on the set {1, 2, 3} is O reflexive,…

A: Relation