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- Implement in Python / Java Algorithm: Testing for lossless (nonadditive) join property. Input: A universal relation R, a decomposition D = { R1, R2, R3, ….. Rm } of R, and a set F of functional dependencies. 1. Create an initial matrix S with one row i for each relation in Ri in D, and one column j for each attribute Aj in R. 2. Set S(i, j) := bij for all matrix entries. (* each bij is a distinct symbol associated with indices (i, j) * ) {for each column j representing attribute Aj {if (relation Ri includes attribute Aj ) then set S(I, j):=aj;};}; (* each aj is a distinct symbol associated with index (j) *) 3. For each row i representing relation schema Ri {for each functional dependency X → Y in F {for all rows in S which have the same symbols in the columns corresponding to attributes in X {make the symbols in each column that correspond to an attribute in Y be…Is each of the following statements true or false? Please explain. a. If a signature σ is infinite (i.e. contains infinitely many symbols), then a σ-formula can have infinite length. b. Let σ := (c, f, ·, <) be a signature, where c is a contant symbol, f is a unary operation symbol, · is a binary operation symbol, and < is a binary relation symbol. Then ϕ(y, z) := ∀x(f(x) · c < x) is an extended σ-formula whose interpretation in each σ-structure is a binary relation. c. For any signature σ and any σ-structure A := (A, σA), if a set D ⊆ Ak is definable (A-definable here), then it is P-definable for some finite P ⊆ A.Help!!! SOS Given the schema S= < { A,B,C,D,E,G,H }, F>, where F represents the following dependencies: AB→D A→D E→B B→H H→C E→C EB→GH E→ G Find a minimal cover for this schema. Find a key for this schema. Find a third normal form decomposition for this schema. Find a BCN form decomposition for this schema.
- let S = {s1, s2, s3, s4, s5}. Give an example of an equivalence relation R on S such that S/R has three elements and one equivalence class of R has at least three elements. Justify your example is correct by listing all of the elements of S/R and all of the elements in each equivalence class of R.Let a bus timetable be represented by a list of routes where each route is repre- sented by Start/End/DepatureTime/ArrivalTime. Both DepartureTime and ArrivalTime are represented by a relation time(Hour,Minutes). Write a Prolog relation journey(Start, End) that is true if there is a route in the timetable that can get a passenger from Startto End directly or any number of intermediate stops where there is at least 10 minutes between the arrival at an intermediate point before the departure of the next leg of the journey. Assume the clock is a 24 hour clock and all departure and arrival times occur within the same day.Assume a generic recursive relation is defined as : A[i] = p*A[i-1] + q where p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list, such as [A[0], A[1], A[2]] and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series: A[i] = A[i-1] + 2 where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case. Phyton
- Assume a generic recursive relation is defined as : A[i] = p*A[i-1] + q where p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list, such as [A[0], A[1], A[2]] and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series: A[i] = A[i-1] + 2 where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case. """ def recursionSolver(values): return # Remove this line to answer this question.Assume a generic recursive relation is defined as :A[i] = p*A[i-1] + qwhere p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list,such as [A[0], A[1], A[2]]and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series:A[i] = A[i-1] + 2where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case.""" def recursionSolver(values):return # Remove this line to answer this question. İn python.def transitiveclosure(g): """computes the transitive closure of a graph/relation encoded as as a set of 2-tuples""" transitiveclosure: This function should accept sets/frozensets of 2-tuples that encode relations, or equivalently, graphs, and should return the least relation that includes the input relation and is transitive: its transitive closure. E.g., an input frozenset({(1,2),(2,3)}) could correctly result in the value frozenset({(1,2),(2,3),(1,3)}).
- can i get some help with this algebric question For each of the following questions write only the answer and you do not need to justify your answers Q 2 Construct the Hasse diagram for the “subset” relation, ⊆ on the setP ({a, b, c}).Q 3 Find the total number of binary operations on a set containing 100 elements.Q 4 Give an example of a monoid which is not group.Q 5 Give an example of a groupoid which is not a quasigroup.Transitive-Closure Input: a list of pairs, L. Interpreting L as a binary relation, Transitive-Closure should return the transitive closure of L. Examples: (Transitive-Closure '((a b) (b c) (a c))) ---> '((a b) (b c) (a c)) (Transitive-Closure '((a a) (b b) (c c))) ---> '((a a) (b b) (c c)) (Transitive-Closure '((a b) (b a))) ---> '((a b) (b a) (a a) (b b))) (Transitive-Closure '((a b) (b a) (a a))) ---> '((a b) (b a) (a a) (b b)) (Transitive-Closure '((a b) (b a) (a a) (b b))) ---> '((a b) (b a) (a a) (b b)) (Transitive-Closure '()) ---> '()Quantifiers are called quantifiers because they express somethingabout the number of elements that satisfy a certain property. Showhow to express the following ‘quantified’ statements in predicatelogic with a unary relation symbol R. You don’t have to introduceany new quantifiers to do this, although you will need to keep inmind that the atomic formula x=yis always considered to be partof the language.(a) Exactly one x satisfies R(x).(b) At least one x satisfies R(x). (c) No more than three x satisfy R(x).(d) All but one x satisfy R(x).