Relations Given the sets over the domain {a, b, c, d}: A = { (a, a), (b, b), (d, d), (b, a) } B = { (a, c), (c, c), (c, a), (d, a) } C = { (a, c), (a, d), (c, b), (c, c) } For A, B, and C: find the following closures. 1. Reflexive 2. Symmetric 3. Transitive Logic

Q: Prave that for all sets A and B, (ANB) = A UBC %3D

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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 :

Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

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Q: 11. Let R₁ and R₂ be the relations on {1,2,3,4} given by R₁ = {(1,1), (1,2), (3,4), (4,2)} R₂ =…

A: Sol:- To find R1 o R2, we need to compose the two relations. The composition of relations R1 and R2…

Q: Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation,…

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Q: List down the elements of A = = {x|x²<45,x € Z} A) {0, 1, 2, 3, 4, 5, 6} B {-6, -5, -4, -3, -2, -1,…

A: The objective is to list down the elements of A.

Q: R relation for A = {a, b, c, d, e, f} partially ordered set and subset B = {b, c, d} Let R = {(b,…

A: Given data: R=b,a,c,d,d,b,e,c,f,d,e,d,f,c which is relation for A=a,b,c,d,e,f partially ordered set…

Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Which of the following sets spans R? R32 O (3,0,-2)} O(3,0-2).(0,0,0)} O(3,0,-2).(5,1,0),(0,-1,1)} O…

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Q: Given set A={1,2,3,4,5} and a relation R on set A, R = {(1,2), (1,3), (2,2), (2,4), (3,1), (3,5),…

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Let X = (1, 2, 3, 4, 5, 6) and let T1= (X, 4, {3}, (1,2,3), (2,3,4), {2}} and T2 = {X, 4, (2),…

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Q: Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10),

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Q: For each part, write the set in the form [x | P(x)] (property that describes the elements of the…

A: Explained below

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: 4. Let A = (1,2,3} and B= {1,2,3,4). The relations R, = {(1,1),(2,1),(3,2)} and…

A: Since you have posted multiple subparts we solve first three subparts for you To get the solution of…

Q: Show that if S x T is a closed subset of R2, then S and T are closed subsets of R.

A: As per the question we are given two subsets of R i.e. S &amp; T and we know that the set S × T is…

Q: Identify the missing ordered pairs from the given list. The list of all ordered pairs in the given…

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Q: Let A = {1,2,3} and let R= {(1,1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 2)} C A x A. In each case,…

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Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: "Consider the relations R₁, R₂, R3 R4 R5 on A = {1, 2, 3, 4} defined by R₁ = {(1, 2), (2, 1)} R₂=…

A: A relation R on the set A={1,2,3,4} is reflexive if (1,1),(2,2),(3,3),(4,4) are all elements of R.…

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…

A: Given (R∪S)-T The solution for (R∪S) is as follows ∪(a,b,c)←R(a,b,c) OR S(a,b,c)--------(i) The…

Q: (b) The domain is fa, b, e, d, e, f). The relation is the set: (b, e), (b, d). (c, a), (c. S). (a,…

A: Given: The relation of a set a, b, c, d, e, f is b, e, b, d, c, a, c, f, a, f, a, a, b, b, c, c, d,…

Q: Suppose f : B C where B = {a, b, c}, C = {2, 8, 10}, and f is defined by f = {(a, 8), (b, 10), (c,…

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Q: A = {1, 2, 3, 4} B = {2, 4, 6, 8} 26. Conjoining strings {(x,x) & A} 27. String concatenation {(x,…

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Q: Prove: For all sets A, B and C, An (B-C) = (ANB) - (ANC).

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Q: Find the union of each of the following pairs of sets :(i) X = {1, 3, 5} Y = {1, 2, 3}(ii) A = [ a,…

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Q: Let S be the set {a,b.c} and the relation R on S is…

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Q: Let A = {1, 2, 3, 4, 5} and R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2,…

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