For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. A binary relation R ⊆ A × A Briefly explain the meaning of the following relation, providing an example (and diagram) in each case: (i)Reflexive (ii) Symmetric (iii) Transitive

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

A:

Q: Write a computer algorithm, in pseudocode, to test whether a relation R defined on a finite set A is…

A:

Q: Let a bus timetable be represented by a list of routes where each route is repre- sented by…

A: I Have answered this question in step 2.

Q: Transitive-Closure Input: a list of pairs, L. Interpreting L as a binary relation,…

A: Transitive Closure is the accessibility matrix to get from vertex u to vertex v of a graph. Given a…

Q: Consider a schema R, a set F of functional dependencies on R, and two candidate keys (k1, k2) as…

A: Given information: - R is schema in which F is a set of functional dependencies two candidate keys…

Q: c) Consider the following relation R with the functional dependencies: AC B, AD E, AB C, E→F, BC A,…

A: Given functional dependencies, AC→BAD→EAB→CE→FBC→AB→D

Q: Consider the relation R(S, N, R, C, J, H, L) and its set of dependencies F = {S, N -> C ; J, H, C ->…

A: using Armstrong's axioms=> proved in figure figure 1:

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: Given set A = {a, b, c, d} show the equivalence relation, which contains eight ordered pairs,…

A: Answer is in step 2

Q: Draw a directed graph for that partial order relation that is defined on a definite set that…

A: Let us draw the directed graph for the partial order relation for the power set.  The power set of…

Q: Consider the relation R = {(1,3), (3,1), (2, 3), (3, 3), (3, 4), (4, 4), (4, 1)} on set {1, 2, 3,…

A: The Answer is

Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is…

A: Option ATransitive.

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: 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: Q6) Let A = Z, the set of all positive integers, and we define the relation R on A as: a Rb if and…

A:

Q: Let A equal the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of…

A: A = { 0000, 1000, 0100, 0010, 0001,            1100, 1010,  1001, 0110, 0101,            0011, 2000,…

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: State what the set is and how the partial order is defined. Show that the relation satisfies the…

A: an example of a partial order relation that is defined on a finite set that contains at least ten…

Q: Suppose relation R is defined as two-dimensional matrix A. Give a pseudo-code for transitive…

A: A)THE BELOW ANSWER IS FOR BOTH PARTS IN THE QUESTION: #include &lt;bits/stdc++.h&gt;using namespace…

Q: Consider a schema R and a set F of functional dependencies as follows: R = (A,B,C,D,E). F = {A →…

A: To check for lossless join decomposition using functional dependency, the following set of the…

Q: Let's suppose, a relation R=(A, B, C, D, E. H) with a set of functional dependencies F: (AE->BC, B…

A: Functional dependency is a DBMS concept . In this attributes of relations  are dependent on each…

Q: Let the set A = { 0, 1,2,3,4,5} and let the relation R be defined on A as : R ={(a, b)ÎA: a divides…

A: A.  The ordered pair item of relation is {(1,1),(1, 2), (1, 3), (1, 4), (1, 5), (2, 2)…

Q: Give an example of a partial order relation with at least 10 components that is defined on a finite…

A: an example of a partial order relation that is defined on a finite set that contains at least ten…

Q: is an ordered *.collection of objects relation set non of them O

A: According the Question below the Solution:

Q: Task 4: Consider the relation schema R(A, B, C, D, E) with the following FDs FD1: {A,B,C} → {D,E}…

A: A)  A relation is said to be in BCNF if all it's functional dependency is of form X-&gt;Y where X is…

Q: Consider the following B+-tree index built for a relation instance using the id as the set of ey…

A: this Question is a Non Leaf Node.   before  3 4 5 6 10 17 18 29 after insert  1 3 4 5 6 10 17 18 22…

Q: Let A = {a, b, c}. a) Give an example of a relation on A that is reflexive and symmetric, but is not…

A: Let A={4,6,8}Define a relation R on A as:A={(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)}Relation R is…

Q: a) Give an interpretation that is a model of A. You must mapp and q to different relations. b) Show…

A: Predicate Quantifiers is used in system modelling &amp; Design

Q: Let R be the relation on A = {1,2,3,4,5} where R = {(1,1),(1,3),(1,4),(2,2),(3,1),(3,3),(3,4),…

A: Here is the solution which is mentioned below:

Q: Assume the relation R over the set {0,1,2,3,4,5,6,7,8,9} where (a,b) ∈ R if and only if
 a+b < 10.…

A: 1. R is not a reflexive relation,because a+b&lt;10; therefore (9,9) does not exist; -&gt; it is…

Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs,t E S, sRt +…

A: Given: s, t are elements of S.

Q: Consider the following sets:               A={2,4,5} B = {4,9,10,12} C = {1,3,8,9,10,12,14}   I)…

A: Answer: Given that A = { 2,4,5 } B = {4,9,10,12} C = {1,3,8,9,10,12,14} Here we will get for AUB is…

Q: Let R1, R2,…, Rn be a decomposition of schema U. Let u(U) be a relation, andlet ri = ΠRI(u). Show…

A: Given,  R1, R2,…, Rn be a decomposition of schema U u(U) is a relation ri = ΠRI

Q: 5. Let R1 and R2 be the relations on {1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 =…

A: Question 5:  a)The elements of R1°R2 and R2°R1 are as shown below:

Q: Given set A={1,2,3,4,5} and let R and S be a binary relation on set A. R = {(a, b) e AxA | b|a} and…

A:

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: 3. (MS) Consider the relation R6 on P({0,1,2, 3}) such that (A, B) e R6 if and only if A C B. Select…

A: This is of discrete mathematics

Q: Consider the relation R(S, N, R, C, J, H, L) and its set of dependencies. F = {S, N -> C ; J, H, C…

A: In given question, we have to show that Functional dependency J,H,S,N→R using Armstrong's axioms. We…

Q: Suppose that we decompose the schema R = (A, B, C, D, E) into (A, B, C) (A, D, E). Show that this…

A: The given functional dependencies are as follows. A → BCCD → EB → DE → A   Consider the decomposed…

Q: Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S,…

A: Reflexive Transitive Closure is the accessibility matrix to get from vertex u to vertex v of a…

Q: Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number…

A:

Q: Suppose we define a relation on the set {strings in A} by making aRb + length(a) = length(b) Support…

A: Let first understand what is Equivalence relations ? A relation on set A is called an equivalence…

Q: The symmetric closure of the relation R={(1,1),(1,2),(2,2),(2,3)(4,4)} on the set {1,2,3,4} is:…

A: We have given a relation R on set {1,2,3,4} and we have to find out the symmetric closure of…

Q: Let A = {x, y} ; B = {1,2,3}; and C = {a, b}, then `A B×C=.. إجابتك Let A and B be two sets. We say…

A:

Q: Implement the following Racket functions: Symmetric-Closure Input: a list of pairs, L.…

A: The code is shown below. It uses the symm helper and opp functions. (define (opp p) (list (car (cdr…

Q: Let A is a set defined as A= {1,2,3,4} and R is a relation on A, R is: * O neither equivalent nor…

A: Let A is a set defined as A= (1,2,3,4) and R is a relation onA, Ris: * neither equivalent nor…

Q: pAp Consider the partal order on the set X(a. b.c.d.e.1)with the following relations aくも くe もくe もく。…

A: Given set is, X={a, b, c, d, e, f} Given partial order sets are: a&lt;=b, a&lt;=c, b&lt;=c, b&lt;=d,…

Q: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also symmetric? Is R1 ∩ R2…

A: