Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a relation on set A. Find the equivalences classes of relation R.

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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

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Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,b),(b,b),(b,c)(c,a)(c,c) and…

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, a),…

Q: Let A = {1, 2, 3, 4, ..., 23} and define a relation R on A as follows: For all x, y € A, x R y =…

A: Solution is in next step

Q: Let S be the set {a,b,c,d} and the relation R on S is {(a,a),(a,b),(b,b),(c,c),(b,c),(a,c)}. then,…

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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: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

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: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

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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: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c   The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: Let {2,3,4}{2,3,4} and {8,9,10}{8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and…

A: Given that:                      A={2,3,4}B={8,9,10}H is an relation from A to B such that: (x, y)∈H…

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

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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: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: Given R = {(m, m), (s, s), (e, e), (m, e), (s, e), (s, m), (e, m)} is a relation on set A = {m, e,…

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Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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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: 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 A = {a, b, c, d, e} and define an equivalence relation R C A × A on the set A as follows: R =…

A: We will answer the first question as you didn't specify any. Please resubmit the other question…

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 {2,3,4} {2,3,4} and {8,9,10} {8,9,10}. Define a relation H from A to B such that (x,y)∈H(x,y)∈H…

A: Given A={2,3,4} B={8,9,10}

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 A = {1, 2, 3, 4}. Give an example of a relation on A that is: %3D (a) reflexive and symmetric…

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Q: Let A = {a, b, c, d}, and R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} be a…

A: A = {a, b, c, d} R = {(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d)} Equivalence…

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

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Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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Q: Let A = {3, 5, 6} ,R relation on A defined by R = {(a, b) : a < b, a, b e A}. rit O a. {(5,3),…

A: If A= {3, 5,6} , Where R = {(a, b) : a&lt;b, a, b€A) } Find 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 A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if…

A: Let A be a non empty set, A relation R on A is said to be an equivalent relation if  1) R is…

Q: Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and…

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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: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

Q: 2. Given a relation, R on A = {a, b, c, d} on as follows: %3D R = {(a, a), (a, b), (a, d), (b, b),…

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Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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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 A = (0, 1, -1, 2} , R relation on A defined by R = {(a, b) : b= a², a, bE€ A}. Write R. %3D

A: Given ,  Let A = {0 , 1 , -1 , 2}  R relation on A defined by  R = {(a , b) : b = a2 , a , b € A} We…