Problem 12 Let A = [0, 10] CR. Let R be a relation on A given by [(a, b) = R E a, b are integers (c, c) € R c is not an integer In other words if (a, b) ≤ R, then either a and b are two integers, and for a non-integers c we only have (c, c) € R. So (2,3), (8,5), and 3.2, 3.2) are in R, but (3.2, 4.5) R. Find the equivalence classes and draw a picture that represents the quotient set A/R.

Q: R = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}

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

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Q: 6.A. Let A = (1, 2, 3) and B = (1, 2, 3, 4) and define a relation R from A to B as Given any (x. y)…

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Q: 3. a. If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows:…

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

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…

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Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following is a relation on X? O [1, 2), (3, 4), (5, 6}} O…

A: Here we have X={1,2,3,4,5,6} We have to determine the relation on X.  A relation defines the…

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: {2, 4, 6, 8} and define a relation R from A to Bas follows: for all (x,y) E AX B, (x, y) ER T. set…

A: As per our guidelines we are supposed answer only 3 subparts and rest can be reposted Given Data:…

Q: 11. Let R₁ and R₂ be the relations on {1,2,3,4} given by R₁ = {(1,1), (1,2), (3,4), (4,2)) R₂ =…

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Q: 1. Let A= {2, 3, 4} and B={6,8, 10} and define a relation Rfrom Ato Bas follows: For all (x, y) E AX…

A: If X=a, b and y=c, d, then X×Y=a,c, a,d, b, c, b, d.  Let R be a relation defined as R=x, y| x,…

Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…

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Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

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Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

Q: 4. Determine which properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does…

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Q: 2. Let A = {1,2, 3}, B = {4,5, 6}, R = {(1,4), (1, 5), (2,5), (3, 6), and || %3D S = {(4,5), (4, 6),…

A: Given set in the question are  A=1,2,3B=4,5,6R=(1,4),(1,5),(2,5),(3,6)S=(4,5),(4,6),(5,4),(6,6)Then…

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…

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Q: Problem 7. A relation is defined on the set of positive integers N by n ~ m if either n divides m or…

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Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…

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Q: 9. List the ordered pairs in the equivalence relation on A = {1, 2, 3, 4, 5} associated with these…

A: Equivalence relation is relatuon which is reflexive, symmetric and transitive.

Q: 5. Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For…

A: Given: A={6, 8, 10, 15, 17} B={2, 3, 4, 5} Relation R:A→B is: For all x,y∈A×B∈R if and only if…

Q: Define the relation r on S = {A, B, C, D} by r ={ (A,B), A,D), (B,A), (B,C), (C,A), (C,B), (D,B)}.…

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