Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U {(a, b) , (b, a) , (b, c) , (c, b) , (a, c) , (c, a) , (d, e) , (e, d)} , H = IAU {(b, c) , (c, b)} . Clearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H, (A/H)/(G/H).

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

A: Given that  A=1, 2, 3, 4, 5, 6 and consider the following equivalence relation on A: R=1,1, 2,2,…

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: 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: Let A = {0, 1, 2, 3} and define relations R, S, and T on A as follows: %3D R = {(0, 0), (0, 1), (0,…

A: Let us first define the relations in this case, Reflexive : A set is reflexive if for a element in a…

Q: Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence…

A: P={{a,b,d},{c,f},{e,g}} . The  equivalence relation is as follows:…

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: Which of the following points is not found in quadrant II? а. (-2, 1) b. P(-225 degrees) с. (2, -1)…

A: In two dimensional Cartesian coordinate system, two number lines are bisected perpendicularly at…

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: PROBLEM 7 art 1. The drawing below shows a Hasse diagram for a partial order on the set A, B, C, D,…

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

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Q: Let T be the function T: R³ R2 given by + (1)-[*] (ED) T (a) Show that T is a linear transformation.…

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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: 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: 1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

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Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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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…