(24 pts) Either show the following relations are equivalence relations, or show which qualities of an equivalence relation they lack: a. S = {0,1,2,3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} b. S is the set of all dog owners. R = {(a, b): a and b own the same breed of dog}

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1, 2} defined by (a, b)S(c, d) if and…

A: S=0,1,2,3×0,1,2=0,0;0,1;0,21.0;1,1;1,22.0;2,1;2,23.0;3,1;3,2

Q: (a) Define relations S and R on the set A = {a,b, c, d} as follows: S = {(a, b), (b, c), (c, d), (b,…

A: Given problem is :

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A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

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Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: 3) a) Suppose A = {0,1,2,3,4} and R = {(0,0). (0,4).(1.1), (1,3).(2,2).(3,1).(3,3),(4,0).(4,4)} is…

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Q: Consider the following relation on {1,2,3,4}. Check is equivalence or not? R= {(1, 1), (1, 2), (2,…

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Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

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A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

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

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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…

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Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

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Q: 6. Q6; Relations (a) Define relations S and R on the set A = {a, b, c, d} as follows: S = {(a, b),…

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Q: prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive…

A: A=a,b,cR=a,a, b,b, c,c, a,b, a,c, c,b A relation R is reflexive if a,a∈R for every element a. Here…

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