Let R be an equivalence relation on A = {3, 4, 6, 7,8, 9} and R = {(8,3), (3, 8), (8, 8), (3, 3), (4, 4), (9,9), (9, 7), (9, 6), (7,9), (7, 7), (7, 6), (6,9), (6, 7), (6, 6)}- Show the partition of A defined by the equivalence classes of R.

Q: Let A = {0,1,2,3} and R be the relation on A given by R =…

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Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

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: Let R be the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6} R= {(1, 1), (1, 5),…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements 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: Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation…

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Q: Let R be a relation on A = {1, 2, 3, 6} and R = {(1,6), (1, 1), (3, 3), (6, 1), (1,2), (2, 1), (2,…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: 7. Let R be the following equivalence relation on the set A = {1,2,3,4,5,6};: R = {(1,1),(1,5),…

A: Equivalence class of R= R  =a=x∈A :aRx 1=1,52=2,3,63=2,3,64=45=1,56=2,3,6

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

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

Q: Let R be a relation on A = {2, 7, 8, 9} and R = {(8,8), (9, 9), (8, 2), (7, 7), (2, 2), (2,7)}. Are…

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

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

A: The set A is defined as: A = {-5, -4, -3, -2, -1, 0, 1, 2, 3 4} x R y ⇔ 3|(x − y). R is an…

Q: A = {1,2,3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1),(2,3),(3,2)}, then R is:

A: If A = {1,2,3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1),(2,3),(3,2)}, then R is:

Q: ) Let A = {1,2,3, 4} × {1,2, 3, 4}, and define a relation R on A by (1, Yı)R(x2, Y2) if r1 + y1 = x2…

A: Equivalence relation means it should satisfy reflexive, symmetric, Transitive conditions.…

Q: Let X = {1, 2, 3, 4}. Let R = {(1, 3), (2, 1), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (a, b) },…

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Q: Let R be the relation on the set {1,2,3,4} containing th (1,2), (1,4), (2,1), (2,2), (2,3), (3,1),…

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

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Q: Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the…

A: Given: A={1, 2, 3, 4, 5, 6, 7} and R is the relation on this set defined s: (a, b)ϵR of the integer…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

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Q: Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,1), (1,2), (1,3), (2,3),…

A: Relation R^2 is nothing but R∘R. Then required relation is given by composition of R and R.

Q: Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (1, 2), (2, 3), (1, 3),(3, 3)}.…

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct option  Explanation…

Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

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: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

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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: let A={0,1,2}. let R = { (0,0),(1,1),(2,2),(0,1),(1,0)}. Is R an equivalnce relation on A?if it is…

A: Given: A=0,1,2 The relation R on set A is defined by R=0,0,1,1,2,2,0,1,1,0 To determine: Whether R…

Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

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Q: Let R be a relation on A = {5, 6, 8, 9} and R {(8,8), (5,5), (6, 8), (5, 9), (9, 9), (9,5), (6, 6)}.…

A: Given that  R=(8, 8), (5, 5), (6, 8), (5, 9), (9, 9), (9, 5), (6, 6)

Q: Let A = (-2, -1, 0, 1, 2, 3, 4, 5, 6, 7} and define a relation R on A as follows: For all x, y E A,…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: A relation R is called reflexive on a set A if (x,x) is in R for all x in A. A relation R' is called…

Q: 9.25. Let A = {1, 2, 3, 4, 5, 6}. The relation R = {(1,1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2),…

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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: Let R be a relation on A = {1, 2, 6, 7} and R = {(6,6), (2,2), (7, 1), (1, 1), (7,7), (1,7)}. Are…

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Q: Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7,8), (8,9), (9, 9), (7, 7), (8, 8),…

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Q: Write A here: A =. Let R be the relation on {0, 1, 2,3, 4, 5, 6, 7,8, 9} given by: (0,0), (0, 1),…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

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: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the…

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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),…

A: