Côñšidéř thé rélátión S on the set {a, 0, C} given by S = { (a, a), (a, b), (b, a), (b, b), (c, c), (b, c), (c, b) } i. Prove S is reflexive. ii. Prove S is symmetric. iii. Show S is not an equivalence relation.

Q: Given the set A- {a, b, c, d} a) If this is the relation R= {(a, b), (b, d)} Show s(R). b) If this…

A: Given R=a,b,b,d. The Symmetric closure of R denoted by sR=R∪R-1, where R-1 is the inverse of the…

Q: 1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b, a)} on set A = {a,b,c,d}. Is…

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

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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: Consider the relation R= {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)} on the set A = {a,b,c}. Is…

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

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Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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

A: Given that   be a relation on the set Reflexive:  For every…

Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…

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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…

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: 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…