1. Suppose that you have the relation R with n tuples and the relation S with k tuples without tuples duplication. How many tuples in final relation result if you apply Union operation? n+k k n n*k
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A: Answer is given below .
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A: In questions with many parts, we must answer the first one.
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A: The Answer is in Below Steps
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A: FALSE
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A: Answer to the above question is in step2.
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A: Given:
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A: ANSWER:
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- Implement the following Racket functions: Reflexive-Closure Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S, Reflexive-Closure should return the reflexive closure of L. In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R. (https://en.wikipedia.org/wiki/Reflexive_closure) Examples: (Reflexive-Closure '((a a) (b b) (c c)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (b b)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (a b) (b b) (b c)) '(a b c)) ---> ((a a) (a b) (b b) (b c) (c c)) (Reflexive? '() '(a b c)) ---> '((a a) (b b) (c c)) You must use recursion, and not iteration. You may not use side-effects (e.g. set!).Implement the following Racket functions: 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 '()) ---> '() You must use recursion, and not iteration. You may not use side-effects (e.g. set!).Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R to be Transitive with Set S
- Design a data structure for a set in which insertions, deletions, and membership queries can be processed in O(1) tim e in the worst case. You m ay assume that the set elements are integers drawn from a finite set {1, 2,...,n}.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)}).Let S be a set with |S| = 5. How many relations are there on S? A. 5! В. 55 C. 520 D. 525 Е. 225 A В E C.
- Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number of tuples that the results of the following expression can have? RUS A. n*m B. n+m C. max{n,m} D. 0 E. min{n,m} F. n-m G. n H. mM is the matrix representation of a relation R on A. A has n elements. M is a n x n matrix. M contains how many 1s and 0s if R is a rooted (directed) tree?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…
- AB* tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk blocks are of size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice of the degree (i.e. the number of pointers per node) of the Bt - tree?Let A={1,2,3} and B={4,5,6}. The set X={(1,4),(3,6),(2,4),(1,5)} is: O a relation between from A to B, but NOT a function from A to B O a set that has nothing to with A and B O equal to AxB O a function from A to BThe domain for the relation R is the set of all integers. For any two integers, x and y, xRy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) Symmetric Transitive Anti-symmetric Reflexive