7. Let S = {1,2,3, ...,8}. Let R be the relation on S defined by the following: %3D xRy + xy is a perfect square a. Find all the coordinate pairs in the relation R. b. Draw a directed graph for R. c. If R is an equivalence relation, find all the distinct equivalence classes. If R is not an equivalence relation, state exactly which property(s) it fails and include specific examples.

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: Let R be a relation from A to B and defined "x is at least twice as big as y." Write R as a set of…

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Q: Please show the following question in detail, I don't understand one bit of it, " Let R be a…

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides…

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Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: Define the relation r on S = {A, B, C, D} by r ={ (A,B), A,D), (B,A), (B,C), (C,A), (C,B), (D,B)}.…

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Q: 4. Let G = {–2, 0, 2} and H = {4,6, 8} and define a relation V from G to H as follows: For all (x,…

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Q: 1. Let A = {2, 3, 4, 5, 6} and B = {10, 11, 12, 13). Define a relation R on (A x B) as follows: a Rb…

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Q: Define: what is an equivalence relation?

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