p.609, icon at Example 2 # 2. Let A be the set of all points in the plane with the origin removed. That is, Define a relation on A by the rule: A = {(x, y)|x, y = R} - {(0,0)}. (a, b)R(c, d) ↔ (a, b) and (c, d) lie on the same line through the origin. (a) Prove that R is an equivalence relation. (b) Describe the equivalence classes arising from the equivalence relation R in part (a). (c) If A is replaced by the entire plane, is R an equivalence relation?

Q: Let X = {0, 1}. (a) List (as subsets of X X X) all possible relations on X. This answer has not been…

A:

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: Which of the followings can possibly be a canonical cover Fc of a set F of functional dependencies?…

A: The answer to this question is option b) {A → D, AB → C, D → B} and d) {A → C, D → B, AB → C}

Q: Given the relation U below, use ordered pair notation to express the relation U o U. U o U = { Ex:…

A: To express the relation UoU (composition of relations U and U), find all pairs (x, y) such that…

Q: Let R be a relation on A = {0, 2, 3, 7} and R = {(7,7), (3, 3), (0, 2), (2, 0), (2, 2), (0, 0)}. Are…

A: SOLUTION- Given, A ={0,2,37} and R={(7,7),(3,3),(0,2),(2,0),(2,2),(0,0)} 1)True  A  relation R…

Q: define functions

A: Given :- In the above given question, the statement is mention in the above given question   Need to…

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: Consider the relation R = {A, B, C, D, E, F, G, H, I,J} and the set of functional dependencies F = {…

A: f ={     AB → C,      A → D,      B → F,  F → GH,  D → IJ   } To find the key check the RHS of the…

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: Let R(A, B, C, D, E, F) be a relation with FD's: {D→ CE, C-→ BDE, E→ AD, AF→ E, B→ D}. Which of the…

A: The given functional dependency is, { D -> CE , C -> BDE , E -> AD , AF -> E , B -> D…

Q: Find a minimal cover in a standard form for the relation schema R(A, B,C, D, E, F, G, H) with the…

A: A minimal cover or canonical cover means a minimum set of functional dependencies. A canonical cover…

Q: 3. R is a binary relation over N, the set of natural integers. (x, y) € R iff x mod 7 = y mod 7. R…

A: Binary Relation:A binary relation is a mathematical concept that defines a relationship between two…

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. 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: Define a relation as follows: ARA = {(a, b) , (a, c), (b, c)} Select the properties that the…

A: Answer to the above question is in step2.

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: Indicate the properties of each of the following relations. For each relation, indicate whether it…

A: here are the properties of each relation:R is reflexive, symmetric, and transitive.R is…

Q: We studied different properties of relations like reflexive, symmetric, antisymmetric, transitive.…

A: Lets see the solution in the next steps

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: Consider a relation R={A,B,C,D,E,F,G,H,I} with the set of functional dependencies and determine,…

A: Now we must determine the above definition whether for each FD. Each value is super key or not on…

Q: elp

A: help plz i will rate you  discrete structure

Q: 7. Write an algorithm that receives as input the matrix of a relation R and produces as output the…

A: Answer :-

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: 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 <bits/stdc++.h>using namespace…

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: Consider the relation R = {F, T, D, N, S} and the set of functional dependencies K = {F¬D, {D, T}…

A:

Q: Let R(A, B, C, D, E, F) be a relation with FD's: {D → C, C → D, D → E, C → E, E → AD, AF → E, D →…

A: Let R(A,B,C,D,E,F) be a relation with FD's  :…

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: 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: This question concerns the logical design of a relation schema LOAN describing the borrowing of a…

A: The relation schema:- LOAN(catalogNo, dateOut, memberNo, dateReturn)

Q: Question 5 Let set A = {1, 2, 3} and S is a relation on set A, where S= {(1, 1), (1, 2), (1, 3), (2,…

A: Relation S is said to be transitive as for a,b,c in A, if (a,b) is in R and (b,c) is in S, then…

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

A: Symmetric closure of the set A={a,b,c}