Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a,b) = (a₁, b₁) if a = a₁. (d) (a,b) = (a₁, b₁) if a − b = a₁ − b₁.

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: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

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Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

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Q: R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R…

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Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: Let X = {1, 2, 3, 4}. Let R = {(1, 3), (2, 1), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (a, b) },…

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Q: Let R₁ and R₂ both be equivalence relations. Show by proof or disprove by counterex- ample the…

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Q: Define two relations R, and R2 on set positive integers. R1 = {(a,b) | a > b} and R2= {(a,b)| a² = b…

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Q: Let R(a, b, c), S(a, b, c), and T(a, b, c) be three relations. Write one or more Datalog rules that…

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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 relations are there on the set {a, b}. Show all possible relations on the set {a, b} in…

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