Determine whether the given relation is an equivalent relation on {1,2,3, 4, 5}. If the relation is an equivalence relation, list the equivalence classes (x, y E {1,2, 3, 4, 5} . ) 1. {(1, 1) , (2, 2) , (3, 3) , (4, 4) , (5, 5) , (1, 3) , (3, 1)} 2. {(x, y) | 3 divides x + y}

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

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Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

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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: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

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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: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Please choose the correct answer. Thank you If X={1, 4, 7} and Y={2, 3} and define a relation R…

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Q: Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows:          R = {(1, 1), (1, 2),…

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

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Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Define a relation R, on the set A = (0, 1, 2, 3) as follows. R, = {(0, 0), (0, 1), (1, 1), (1, 2),…

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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. draw a…

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Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

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Q: Let A= {0,1,2,3,4} and a partition of A be: {0,2},{1},{3,4} (a) Write all pairs of the relation…

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Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: Which of the following relations is the Symmetric relation over the set A= {3,5,13}…

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Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

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Q: Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where: ? = {(1,1),…

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Q: а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: Consider the relation R = {(a, a), (c, a), (b, c), (d, b)} then which of the following set…

A: We need to find R3 given R=a,a,c,a,b,c,d,b Now,  R2=RοRR3=RοR2=R2οR The composition of two…

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Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

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Q: 1. Consider the relation R1: R - R such that (r1, y1)R1 (X2, y2) if and only if both points are on…

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Q: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

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Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: Suppose that the relation of H is defined as follows. H= {(9,m), (4,0) (5,m)}   give the domain and…

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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: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: List the ordered pairs in the relation R from A={0,1,2,3,4} to B={0,1,2,3} where (x,y) R if only if…

A: 1. As 0≤0, 0≤1, 0≤2, 0≤3, 1≤1, 1≤2, 1≤3, 2≤2, 2≤3, 3≤3 So the ordered pairs relation is R = {(0, 0),…

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 −…

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Q: 2. 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…

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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: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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Q: In each case below, a relation on the set {1, 2, 3} is given. Of the three properties, reflexivity,…

A: (a) Given relation on the set {1,2,3} is R = {(1,3) ,(3,1),(2,2)} (i) Clearly (1,1) is not belong to…

Q: The domain for a given relation R is the set A = {1,2,3,4). Select the correct description of the…

A: A relation R on set A is called Anti-Symmetric if xRy and yRx implies x=y∀x∈A and ∀y∈A. Example −…

Q: The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: Reflexive Relation: A relation R on a set A is said to be reflexive if  (a,a)∈R   for every a∈A.…

Q: The relation R on set A = {0, 1, 2, 3, 4, 5} is given by R = {(0, 0), (0, 1), (0, 5)(1,0),(1, 1),…

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Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and let S be the relation {(2,1), (3,1),…

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Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

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

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Q: Let C = {1, 3, d, e}. Let R = {(1, 1), (1, 3), (1, e), (3, 3), (3, d), (e, 3) be a relation on C.…

A: The given set is C = {1,3,d,e} and the given relation is R={ (1,1),(1,3),(1,e),(3,3),(3,d),(e,3) }…