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Consider the algorithm in Figure 8.18 to compute -+. Show that this algo-rithm is more efficient than the one presented in Figure 8.8 (Section 8.4.2)and that it computes -+ correctly.8.9 Given the database schema R(a, b, c), and a relation r on the schema R,write an SQL query to test whether the functional dependency b ? c holdson relation r. Also write an SQL assertion that enforces the functional de-pendency; assume that no null values are present. (Although part of theSQL standard, such assertions are not supported by any database imple-mentation currently.)8.10 Our discussion of lossless-join decomposition implicitly assumed that at-tributes on the left-hand side of a functional dependency cannot take onnull values. What could go wrong on decomposition, if this property isviolated?8.11 In the BCNF decomposition algorithm, suppose you use a functional de-pendency -? to decompose a relation schema r(-, , ) into r1(-, )and r2(-, ).a. What primary and foreign-key constraint do you expect to hold onthe decomposed relations?b. Give an example of an inconsistency that can arise due to an erro-neous update, if the foreign-key constraint were not enforced on thedecomposed relations above.c. When a relation is decomposed into 3NF using the algorithm in Sec-tion 8.5.2, what primary and foreign key dependencies would youexpect will hold on the decomposed schema?8.12 Let R1, R2,…, Rn be a decomposition of schema U. Let u(U) be a relation,and let ri = -RI (u). Show thatu ? r1 ? r2 ? ? rn8.13 Show that the decomposition in Practice Exercise 8.1 is not a dependency-preserving decomposition.8.14 Show that it is possible to ensure that a dependency-preserving decom-position into 3NF is a lossless decomposition by guaranteeing that at leastone schema contains a candidate key for the schema being decomposed.(Hint: Show that the join of all the projections onto the schemas of thedecomposition cannot have more tuples than the original relation.)8.15 Give an example of a relation schema R and set F of functional depen-dencies such that there are at least three distinct lossless decompositions ofR into BCNF.Suppose you have a spatial database that supports region queries (withcircular regions) but not nearest-neighbor queries. Describe an algorithmto find the nearest neighbor by making use of multiple region queries.25.4 Suppose you want to store line segments in an R-tree. If a line segment isnot parallel to the axes, the bounding box for it can be large, containing alarge empty area. Describe the effect on performance of having large bounding boxeson queries that ask for line segments intersecting a given region. Briefly describe a technique to improve performance for such queriesand give an example of its benefit. Hint: You can divide segments intosmaller pieces.25.5 Give a recursive procedure to efficiently compute the spatial join of tworelations with R-tree indices. (Hint: Use bounding boxes to check if leafentries under a pair of internal nodes may intersect.)25.6 Describe how the ideas behind the RAID organisation (Section 10.3) canbe used in a broadcast-data environment, where there may occasionallybe noise that prevents reception of part of the data being transmitted.25.7 Define a model of repeatedly broadcast data in which the broadcastmedium is modelled as a virtual disk. Describe how access time and data. text1. [8 pts] A frequency modulationsystem operates with a transmissionbandwidth BEMI-24 A7/z…. … textFigure 1 shows a simplified block diagram of an amplitudemodulator with two different sinusoid input signals: VA(t)and signal Ve(t). Input signal VA(t) has an RMS … … text2. [8 pts] A frequency modulated signalwith carrier frequency fe = 2MHz hasthe form (!) = 10cos(2nfor… …Engineering & TechnologyComputer ScienceCOMPUTER S COMP38411