Let R and S be the following relations: R S А В С 3 1 2 13 2 2 3 1 А C D 13 2 1 2 3 2 3 1 3 2 1 Give tables for the following relations: 1. RAS 2. П[А, В](R) м П[А, С](S) 3. ПА, С](R) — П[А, С](S)
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- Identify each relation on N as one-to-one, one-to-many, many-to-one, or many-to-many. (a) R = {(1, 6) , (1, 4) , (1, 6) , (3, 2) , (3, 4)}(b) R = {(12, 5) , (8, 4) , (6, 3) , (7, 12)}(c) R = {(2, 7) , (8, 4) , (2, 5) , (7, 6) , (10, 1)}(d) R = {(9, 7) , (3, 4) , (3, 6) , (2, 4)}Let r and s be relations with no indices, and assume that the relations are not sorted. Assuming infinite memory, what is the lowest-cost way (in terms of I/O operations) to compute r ⋈ s? What is the amount of memory required for this algorithm?Given the following decompose into tables in BCNF. R=ABC F={A-->C, BC --> A}
- Normalize the following given data to 1/2/3 NF. State the relations schema after everynormalization.Convert the following relation to 2NF, and then to 3NF. Show both conversions. (h, n, c, a, f, k, p, r, g, i, m, b, o, d, j, l, s, e) Functional Dependencies: p → j m, b → l h → g n → p n → o c → i n → j p → o h → d s → e a → rConsider the representation of the ternary relationship of Figure 6.29a usingthe binary relationships illustrated in Figure 6.29b (attributes not shown).Show a simple instance of E, A, B, C, RA, RB, and RC that cannot correspond to any instance of A, B, C, and R.
- Determine which of these relations are reflexive. The variables x,y,x',y' represent integers. A. x~y if and only if x+y is even B. x~y if and only if x+y is odd C. x~y if and only if x+y is positive D. x~y if and only if xy is positive E. x~y if and only if x-y is a multiple of 10Question 21 D={0,1}^6. The following relation has the domain D. Is the following an equivalence relation? Recall that an equivalence relation is reflexive, symmetric and transitive: relation R: xRy if y can be obtained from x by swapping any two bits. True False116. The decomposition of one relation say R into two relations is classified as a. functional decomposition b. ternary decomposition c. binary decomposition d. ordinary decomposition
- Let relations r1(A, B, C) and r2(C, D, E) have the following properties: r1 has20,000 tuples, r2 has 45,000 tuples, 25 tuples of r1 fit on one block, and 30tuples of r2 fit on one block. Estimate the number of block transfers and seeksrequired using each of the following join strategies for r1 ⋈ r2: Block nested-loop join.Let relations r1(A, B, C) and r2(C, D, E) have the following properties: r1 has20,000 tuples, r2 has 45,000 tuples, 25 tuples of r1 fit on one block, and 30tuples of r2 fit on one block. Estimate the number of block transfers and seeksrequired using each of the following join strategies for r1 ⋈ r2: Nested-loop join.Computer Science Given the relation R (A, B, C, D, E, F, G) and the set of functional dependencies: F= {BCD → A, BC → E, A → F, F→G, C→D, A→G}, a) Decompose R into 3NF. Show the different steps. b) Is this decomposition also in BCNF? Why or why not?