Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: R = {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (2, 3), (3, 2), (4, 5), (5,4), (4, 6), (6,4), (5,6), (6,5) List the equivalence classes of R.

Q: Explain why each of the following binary relations on S = {1, 2, 3} is not an equivalence relation…

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Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

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: 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 an equivalence relation on A = {0, 1, 4, 5, 7, 9} and R = {(0, 9), (9, 0), (0, 0), (9, 9),…

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Q: Prove that the following relations are true in general: a. A₁ + A₂=(A₁-A₂) U (A₂-A₁) h AU(A04- (A.)…

A: Given, To prove that the following relations are true in general: a). A1 + A2 = (A1 - A2) U (A2 -…

Q: 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: Let A = {p , q, r, s, t, u, v}, and let R be the following equivalence relation on A: R = { (p, p)…

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Q: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: Let A = {1, 2,3, 4}. The following relation R is an equivalence relation on A: R=…

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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: y) ∈ R mean

A: Given as, A = {4, 5, 6} and B = {5, 6, 7}

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

A: Given that A= { 1 , 2 , 3 , 4 , 5 , 6} And the equivalence relation on A R = { (1,1) ,(2,2) ,(3,3)…

Q: sider the relation R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} on the set {1, 2, 3, 4}. What is the…

A: We have to find transitive closure of R. Where R is R={(1,2),(1,4),(2,3),(3,1),(4,2)} on the set…

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.