A. Let R be the following equivalence relation on the set A = {1, 2, 3,...

 

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A. Let R be the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6): R = {(1, 1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1), (5, 5), (6, 2), (6, 3), (6, 6)}. a. Show that I is an equivalence relation on A. Explain fully how R satisfies all the properties of an equivalence relation. [20 points] b. Find the partition of the set A induced by R; that is, the equivalence classes of R. [15 points] B. Let > be a relation on s={2,3,4,5,6,7,8,9,10} such that if (,y) e then +y is a composite number. If * is an equivalence relation, find the partition of S induced by ; that is, the equivalence classes of *. Otherwise, prove that is not an equivalence relation. [5 points] A. Let R be the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6): R = {(1, 1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1), (5, 5), (6, 2), (6, 3), (6, 6)}. a. Show that I is an equivalence relation on A. Explain fully how R satisfies all the properties of an equivalence relation. [20 points] b. Find the partition of the set A induced by R; that is, the equivalence classes of R. [15 points] B. Let > be a relation on s={2,3,4,5,6,7,8,9,10} such that if (,y) e then +y is a composite number. If * is an equivalence relation, find the partition of S induced by ; that is, the equivalence classes of *. Otherwise, prove that is not an equivalence relation. [5 points]

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A a To show that R is an equivalence relation on A we need to demonstrate that it satisfies three properties reflexivity symmetry and transitivity 1 R... View the full answer