1. List the ordered pairs in the relation R from A = {o, 1, 2, 3, 4} to B = {o, 1, 2, 3}, where(a, b) ER if and only if а) а-Db. b) а+b%3D4. с) а>b. d) al b. e) gcd(a, b) = 1. f) lcm(a, b) = 2.

Q: Definition (hints): a = b(mod m), read "a is congruent to b mod m," if m|(a - b); that is, (a - b)…

A: FALSE

Q: List the ordered pairs in the relation R from A = 0,1, 2, 3, 4, B = 1, 2, 3, 4, 5, where Ris defined…

A: answer to the question is in step2 where a=2b.

Q: List all the ordered pairs in the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6,…

A: Suppose you have a pair of two numbers. You have to find the pairs were a%b = 0 For the given sets,…

Q: Definition (hints): a = b(mod m), read "a is congruent to b mod m," if m|(a - b); that is, %3D (a -…

A: False

Q: 29. The complementary relation R is the set of ordered pairs {(a, b)la,b) € R}. Let R be the…

A: R-bar is the complement of R

Q: 39 of 40 Let R = (A, B, C, D) be a relation schema with the FD's: A → B and B → A. R has how many…

A: There are 3 super keys in given relation that are ABCD ,ACD and BCD

Q: Write the relation matrix for the relation R on the set (a,b.c.d,e.f) which is defined as follows:…

A: Relation Matrix: Any relation can be represent using the matrix representation. The matrix contain…

Q: How many minimal keys this relation has? A B C DE F G 1 4 4 4 2 4 3 2 5 4 4- 2. 4- 2. 3. 4. 2. 3. 4-…

A: Given that how many minimal keys this relation has? actually it required 6 keys to give a relation…

Q: 2. Relation R(a,b) contains the following tuples: (1,2), (1,3), (1,4), (2,3), (3,4). and (4,5).…

A: The Answer is in Below Steps

Q: Let R be the relation on the set {a,b,c,d} containing the ordered pairs (a,a), (a,c), (b,b), (b,c),…

A: Let R is a relation on a set A, that is, R is a relation from a set A to itself. Then R◦R, the…

Q: 1. Suppose that you have the relation R with n tuples and the relation S with k tuples without…

A:

Q: Question 2 Composite relations can be thought of as composite functions. If S is a relation from set…

A: As per guidelines we can answer only one question at a time for answers of other question ask…

Q: The relation R(A,B,C,D,E) has the following functional dependencies. A, B --> C B, C --> D C, D…

A: Answer for (A) and (B):

Q: Given X = {1,3,5}. R1 is a relation on X, defined by aRīb if and only į la – b| is an even integer.…

A: Here in this multi part question.in the first one we have asked to find realtion element and it's…

Q: Consider the following Relation instance of R1(A, B, C, D): A D Null Null 1 Null Null 1 1 Null 1 2 4…

A: A relation stores data about entities using database languages. The structure of a relation is…

Q: B = {1,2,3,4,5,6} Suppose R is relation on BxB with pair (a,b) such that a < b. R is represented as

A: Step 1:- Given:- B = {1,2,3,4,5,6) Suppose R is relation on BxB with pair (a,b) such that a &lt; b.

Q: Walkthrough with n = 12 and A = (3, 5, 8, 8, 9, 16, 29, 41, 50, 63, 64, 67) A[5] = 9, /| A[1] = 3,…

A: Solution ::  Let's first discuss what is algorithm ::  A algorithm is a series of instructions…

Q: Let relations r1(A, B, C) and r2(C, D, E) have the following properties: r1 has20,000 tuples, r2 has…

A: A nested loop join is a naïve algorithm that contains a pair of nested for loops. To perform this…

Q: Walkthrough with n = 12 and A : (3, 5, 8, 8, 9, 16, 29, 41, 50, 63, 64, 67) // A[1] = 3, A[2] = 5,…

A: According to the information given:- We have to find out the target value with the help of algorithm…

Q: You are given a binary relation R (defined below) on A. Each tuple (a, b) indicates that a is…

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: Suppose a relation schema R = (A, B, C, D) is decomposed into following relations R1(A,B,C) and…

A: A relation schema R is decomposed into R1 and R2

Q: Let relations r1(A, B, C) and r2(C, D, E) have the following properties: r1 has20,000 tuples, r2 has…

A: Block nested-loop join: The “r1” needs (20000/25)=800 blocks and “r2” needs (45000/30)=1500 blocks.…

Q: Problem 1 Convert the following relation to 2NF, and then to 3NF. Show both conversions. (h, n, c,…

A: 2NF: A relation is in 2NF if it is already in 1NF and all functional dependencies should be full…

Q: Relative to the ordering 1, 2, 3, 4 the following relation R is transitive. [o 0 1 1] 0 10 0 10 10…

A: To find if the given matrix is transitive or not we have to prove something    MR = M2 R+ MR  No we…

Q: The relation R(A, B, C, D, E) has the following functional dependencies. А, В - С В, С -> D C, D→E…

A: Attached Solution for (a) and (b) part:

Q: 1. Given each relation write down the properties that the relation has. If the relation does not…

A: Below is the answer with explanation:

Q: Show that the following decomposition of the schema R of Exercise 7.1 is not alossless…

A:

Q: Show that the following decomposition of the schema R of Exercise 7.1 is not alossless…

A: Given: Show that the following decomposition of the schema R of Exercise 7.1 is not alossless…

Q: Consider the relation R(A, B, C, D, E), where it is known that the only keys are KA, C, D} and {D,…

A: Functional Dependency: This is a connection between two attributes, wherein the attribute on the…

Q: Draw the Hasse diagram for the relation Ron A = {3,5,7,15,21,35,42,105} wher means a | b (a divides…

A: Hasse Diagram: A Hasse diagram depicts the relationship between elements of a partially ordered set…

Q: Problem 1 Convert the following relation to 2NF, and then to 3NF. Show both conversions. (h, n, c,…

A: In this question, first, we find the 2NF. In 2NF, for relations where the primary key contains…

Q: Suppose you are given a relation R-(A,B,C,D,E) with the following functional dependencies:…

A: Relation R which is defined functional dependencies

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

A: A relation R is reflexive if and only if (a, a) ∈ R , ∀a ∈ A   Here,  A = {a, b, c}   Therefore, (a,…

Q: 2. Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: Answer: 236 or 68719476736

Q: of 40 Let R(A, B, C, D) be a relation with FD's: A → B, C → D, AD → C, and BC → A. If we decompose R…

A: If we decompose R into BCNF relations,which of the relations will not be present in the…

Q: A decomposition of a relation R into Rị and R2 is dependency preserving, if - (a) R can be…

A: Answer: The correct option is “(d) All of them”

Q: QUESTION 9 A relation R(M, N, O, P, Q) is in 2NF and has the following functional dependencies: • MN…

A: Dear Student, As MN derives O and O derives P and also Q thus MN derives M,N,O,P,Q. Thus MN is a…

Q: 21o of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in…

A: We have a relation R(A,B,C,D,E,F,G) and functional dependencies. We have decompose R into 4…

Q: Given the relation R on the set of all integers defined by the rule (x, y) and only if x 2 y². a) i.…

A: In questions with many parts, we must answer the first one.

Q: Assume that you have the following relation; R(a,b,c) a   b  c ---------- 1  A   F 2  B   M 3…

A: Degree is the total number of attribute/fields of a relationship/table. cardinality is the total…

Q: Suppose you are given a relation R=(A,B,C,D,E) with the following functional dependencies:…

A: Given Suppose you are given a relation R=(A,B,C,D,E) with the following functional dependencies:…

Q: Assume that you have the following relation; R(a,b,c) a   b  c ---------- 1  A   F 2  B   M 3…

A: Projection Operator (π) is a unary operator in relational algebra that performs a projection…

Q: Given a relation R( P, Q, R, S, T, U, V, W, X, Y) and Functional Dependency set FD = { PQ → R, P →…

A: Given: a relation R( P, Q, R, S, T, U, V, W, X, Y) and Functional Dependency set FD = { PQ → R, P →…

Q: Question: Consider the relation: R(A, B, C, D, E, F, G, H, I, J, K, L,M,N,O,P,Q), {A, B} is the…

A: R(A, B, C, D, E, F, G, H, I, J, K, L,M,N,O,P,Q) Candidate key: {A, B}, {C,D,E}Prime attributes Non…

Q: 1 Draw a dependency graph between any two courses from the table given below. Then you need to find…

A: Please find the answer below:

Q: Suppose that you are given a relation R = (A,B,C,D,E) with the followingfunctional dependencies: {CE…

A: CE-&gt;D D-&gt;B C-&gt;A CD-&gt;A Attribute Closure CEA+-&gt;CEADBCEB+-&gt;CEBDACED+-&gt;CEDBA So…

Q: Let R(A, B, C, D) be a relation with FD's: A → B, C → D, AD → C, and BC → A. If we decompose R into…

A: Answer to the above question is in step2.

Q: You are given the following set of functional dependencies for a relation R= (A, B,C,D,E,F), F= (AB…

A: A) The functional dependency are AB-&gt;C DC-&gt;AE E-&gt;F The key for the given relation is set of…

Q: 7. 7 of 40 Suppose R is a Many To One relationship from entity set E1={b1,b2,b3} to…

A: Here, R is Many to One relationship. And we have Relationship R from E1 to E2. Many E1 side and one…

Q: (10) Discrete Structure: Please solve it on urgent basis: Question # 10 :                  For…

A: A = {1,2,3,4}  R = { (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4) } The relation R is not…