Consider a relation R(A, B, C, D, E, F), with FDs AB → C , BC → D, D → E, BE → F and DF → C. 1. Is R in BCNF? Explain why or why not. 2. Find the closure of the following: 1. (A, B) 2. (B, D) 3. (D, F) 3. List one superkey of R that is not a (minimal) key

Q: Let R(ABCDEFG) be a relation and F={A -> C, A-> D, B->F, E->F, F->G} a. Show example of lossless…

A: According to the information given:- We have R(ABCDEFG) F={A -> C, A-> D, B->F, E->F,…

Q: Define two sets: a letter set A = {t. p. c) and a word set B = {proposition, math, proof, discrete).…

A:

Q: Suppose ρ is the relation defined on P({1, 2, 3}) in which, for A, B ∈ P({1, 2, 3}), AρB means "A…

A: Given: P({1, 2, 3}) A, B ∈ P({1, 2, 3}) AρB means "A and B both have exactly 2 elements."  ρ is…

Q: Consider a relation R (A, B, C, D, E, G, H, I, J) and its FD set F = {EC -> B, C->D, ->BH, H->ACD,…

A: 1)  Closure (IJ) ={I,J, E, G, H, A, B, C, D} Closure (EJ)={E, G, H, I, B, A, C, D, J} Thus here key…

Q: Consider the schema R = (A, B, C, D, E, G) and the set F of functional depen- dencies: AB → CD ADE…

A: a. To find the candidate keys of R, we need to determine the attribute closure of every subset of…

Q: p.629, icon at Example 2 # 1. Let R be the relation on {1,2, 3, 4} such that R = {(1, 1), (1, 4),…

A: Step 1: Step 2:

Q: Let R be a relation on A = {0, 2, 7, 8} and R = {(7, 2), (8, 8), (8,0), (2, 7), (2, 2), (7,0)}. Are…

A: The given relation R is defined on the set A = {0, 2, 7, 8}, and R = {(7, 2), (8, 8), (8, 0), (2,…

Q: Given: Relation R = {(a,c), (b,c), (c,c)} and Set S = {a, b, c} %3D Complete Relation R to be…

A: Given: To make the relation R symmetric.

Q: PQ → TY ii. P → QR iii. QST → R iv. STR → P   From the above functional dependencies, using…

A: Given:- i. PQ → TY ii. P → QR iii. QST → R iv. STR → P   From the above functional dependencies,…

Q: 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…

A:

Q: 1) Let F be a set of functional dependencies given as: F = {A'- BC, B → C, A - B, AB → C}; Find…

A:

Q: 1. If we project the relation R(A,B,C,D,E) with dependencies A→→BC, B→D, and C→→E onto S(A,C,E),…

A: Answer is given below-

Q: Decompose R into a set of 3NF relations, that is lossless join and dependency preserving.

A: Here we decompose it in 3nf and check dependency preserving.…

Q: Consider a relation T on Z where T = (1,1)}. Is T reflexive? Is T symmetric? Is T transitive?…

A: Given a relation T on Z T={(1,1)}   T is not reflexive because Z is integer and has many element so…

Q: Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) 5. Find a 3NF…

A: The given Functional depenency are :  F = {BC -> D, B -> E, CE -> D, E -> CA, BF ->…

Q: For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2),…

A: Brief explanation about Reflexive, Symmetric and Transitive is presented here:-

Q: Suppose that R is the following relation on the set A = {1,2,3,4}: R = A × A – {(1, 1), (2, 2), (3,…

A: The Cartesian product is a mathematical operation that takes two sets and creates a new set…

Q: For non empty binary relation R={(a, a).(a, b),(b, a).(b, b).(c, C).(C, d).(d, C).(d, d)} on the set…

A:

Q: Let R be the relation R = {(a, b) | a < b} on the set of integers. Find a) R-!. b) R.

A: a)R-1

Q: Minimization of a logical function with Weich maps:  Vm(0,1,2,3,4,5,6,7,10,13)

A:

Q: Let T be the partial order relation on P({1,2,...,20}) defined by ATB if and only if |A| <|B| or…

A: I Have answered this question in step 2.

Q: The relation x ≡ y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

A: A.

Q: Exercise 19.13 Consider a relation R with five attributes ABCDE. 1. For each of the following…

A: (a) { } (i.e., empty relation): does not violate either dependency. (b) {(a,2,3,4,5), (2,a,3,5,5)}:…

Q: Oa.2

A: Here as we can see all vertices have self loop. Thus the relation is = .  Also as we can see there…

Q: The reflexive and transitive closure of the relation A = {(0,1),(1,2)} on B = {0,1,2} is…

A: Here in this question we have given a relation on some set B. and we have asked to find the…

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

A: we will discuss the composition of the given relation in the next step

Q: er the questions

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Q: Let S = {1,2,3}. Let be the relation on S x S defined by (a, b) ≤ (c,d) a ≤ c and b>d (a) Show that…

A:

Q: Define a relation R on Z×Z by (m,n)R(s,t) if and only if m-n = s-t. Is R reflexive? symmetric?…

A: In the given case, we prove all three one by one.

Q: 4. Let A = {1,2,3,4,5,6,7). For all a, b € A, define a~ b if and only if is a power of 2. (a) What…

A: As given that a~b is a/b if it power of 2. So, our relation will…

Q: R = ABCD F3{C-D, C-А, В -С } A. Find all candidate keys. B. What is the strongest normal form that…

A: A) Attribute or set of attribute that can determine all the attribute of relation R is key of R.…

Q: 1. List the ordered pairs in the relation R from A = {o, 1, 2, 3, 4} to B = {o, 1, 2, 3}, where(a,…

A: Summary: In this question, we have been given two sets A and B, and we have to find those relations…