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: 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: A relation R on a set S, defined as x R y if and only if y R x. This is an example of? a) reflexive…

A:

Q: define functions

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

Q: Consider the relation R defined on the set Z x Z: R = {((a,b),(c,d)) | a = c (mod 4) a b = d (mod…

A: given that

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: B.  Draw the digraph of the relation on {a, b, c, d} 1.  {(a, b), (b, b), (b, c), (c, d), (d, a)}…

A: Digraph is a directed graph consists of a set of nodes and set of ordered pairs called edges. Here,…

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: Н.W: Al/ Which of these relations on {0, 1, 2, 3 } are equivalence relations, why? а) R1- {(0, 0),…

A:

Q: Given the relations U and S below, use ordered pair notation to express the relation So U. a b b

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

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: 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: 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: b) Express the following relation using a set-builder notation R = {(1, 2), (2, 6), (3, 9), (4, 16),…

A: Set-builder notation is a mathematical notation for describing a set of representations.

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

A: Lets see the solution in the next steps

Q: Let R be a relation on A = (0, 1,7,9). If (7,9) ER, what must NOT be an element of R for R to be…

A: Let R be a relation on A = {0, 1,7,9). If (7,9) ER, what must NOT be an element of R for R to be…

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

A: Answer :-

Q: lation R on a set S, defined as x R y if and only if y R x. This is an example of? a) reflexive…

A: Introduction: A relation R on a set S, defined as x R y if and only if y R x. This is an example…

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 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: 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: For each of the following pairs of expressions, give instances of relations thatshow the expressions…

A: R = {(1, 2)}, S = {(1, 3)}

Q: Consider the relation R = {(a, d), (b, a), (b, c), (c, b), (c, c), (d, a)} on the set {a, b, c, d}.…

A: Below are the required answers :

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}

Q: let R be a relation defined on the set z by aRb if a < b. What property/properties are violated? A.…

A: EXPLANATION: Any relation R that is defined on a set A can be reflexive or symmetric or transitive…

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

A:

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: Write the reflexive, symmetric and transitive closure of the relation given b B={ c, d}, BRe={(c,c),…

A: reflexive transitive and symmetric closure of the relation