I need answer of : d. Justifying your answer, find the smallest set of related pairs which must beadded to R in order for it to become an equivalence relation. Question 7Let R be the relation on the set S = {1,2,3, a, b, c} given byx Ry if and only if(г, у) € {(а, а), (1,1), (а, 1), (1, а), (3, 1), (1,3), (3, а), (а, 3), (ь, b), (ь, 2), (2, с)}6.(a) Draw a digraph representing the relation R.(b) Show that R is not transitive.(c) Justifying your answer, find the smallest set of related pairs which must beadded to Rin order for it to become transitive.(d) Justifying your answer, find the smallest set of related pairs which must beadded to R in order for it to become an equivalence relation.

We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

Answered: (d) Justifying your answer, find the…

(d) Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become an equivalence relation.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.1: Sets

Problem 29E

See similar textbooks

Related questions

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

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R. Using…

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

Q: The relation on the set of integers R {(x, y) : 5 divides a- y} is O a. an equivalence relation O b.…

Q: R.2. Consider the relation R=- ={x,y):x.yeR&]x=}<3}. Is R an equivalence relation on set of real…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A: By definition of relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

Q: 1. Let A = {0,1,2,3,4,5}. Write out the relation R that expresses greater than orequal on A. Then…

A: Handwriting solution

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition: A reflexive relation is the one in which every element maps to…

Q: 5. when: Let be a relation where R = {(a, b): pair a,b are cross streets in city A}. Sh (a) (a, b) e…

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

Q: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that x is congurent to y mod 4.

Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}. We find an example that shows that R is not…

Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: For each relation, indicate whether the relation is: \ item Reflexive, anti-reflexive, or neither \…

A: (a) From the given data the relation is xLy if x<y. (i)For every x∈ℝ, since x is not less than x…

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

A: (a) Let the set A=set of all watermelons in the truck and R be the relation on A, i.e R⊂A×A defined…

Q: The question I had to solve was: Let S be the set of real numbers. If a, b are elements of S,…

A: Let S is set of all real number. If a, b are elements of S, define a related to b if a-b is an…

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: x R y in R if x- y < 3 |

A: Note that for any real number x, |x-x|=0<3. Thus, xRx or the given relation is reflexive.

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m ∀m∈ℚ…

Q: Essentials of DISCRETE MATHEMATICS Q: Shot that the relation “congruency modulo n” is an…

A: We have to show that the relation “congruency modulo n” is an equivalence relation.

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

Q: Determine whether the following relations are equivalence relations. For those relations that are…

Q: Give the domain and range of the relation. 6) 6) 13 12/ 8. A) domain: (4, 12); range: (5, 13} C)…

Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: As you asked too many questions , I do only first three a)Let V1 = {(x,y)∈ ℤ x ℤ; x + y is an even…

Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is. Chose the correct.(A)…

A: Given,

Q: d. The business major has attended FSU for 4. Let C = (0, 1, 2} and D = (2,4,6, 8) and define a…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric,…

A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

Q: 6. Prove the following statements and provide an illustration to substantiate the proof. a) Let R1…

A: (i), (ii) & (iii) implies R1 intersection R2 is an equivalence relation.

Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

Q: The relation on the set of integers R= {(x,y):5 divides x +y} is O a. none of the choices O b.…

A: Use the relevant definitions.

Q: List the coordinate pairs needed in order to turn the following relations into equivalence…

Q: In N × N clause β for (a,b), (c,d) ∈ N × N defined as: (a,b)β(c,d) = ad = bc Examine the properties…

Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

Q: Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y…

Q: 1. Consider the relation R1 : R2 - R² such that (r1, y1)R1 (x2, y2) if and only if both points are…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

Q: 9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b) , (a, c)} is a relation on S. Which of the…

Question

I need answer of :

d. Justifying your answer, find the smallest set of related pairs which must be
added to R in order for it to become an equivalence relation.

Question 7
Let R be the relation on the set S = {1,2,3, a, b, c} given by
x Ry if and only if
(г, у) € {(а, а), (1,1), (а, 1), (1, а), (3, 1), (1,3), (3, а), (а, 3), (ь, b), (ь, 2), (2, с)}
6.
(a) Draw a digraph representing the relation R.
(b) Show that R is not transitive.
(c) Justifying your answer, find the smallest set of related pairs which must be
added to Rin order for it to become transitive.
(d) Justifying your answer, find the smallest set of related pairs which must be
added to R in order for it to become an equivalence relation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

{(а, 1), (ь, 3), (с, 4), (а, 1), (а, 2)} dan Rz {(w, 2), (w, 4), (y, 1), (z, 4)}. Determine Given two relations R1 R1 x R2.
5) R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S = {(2,1},(3,1),(3,2),(4,2)}. Find S o R, R o S, R-1, S-1,where o means composition.
5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1, 3), (2, 3), (2, 4), (3, 1), (3, 4), (3, 5), (4, 2), (4, 5), (5, 1), (5,2), and (5, 4). Find, a) R² b) R³ c) R4 d) R5
The relation R on set A = {0, 1, 2, 3, 4, 5} is given by R = {(0, 0), (0, 1), (0, 5)(1,0),(1, 1), (1, 5), (2, 2), (2, 4), (3, 3), (4, 2), (4, 4), (5, 0), (5, 1), (5, 5)}. (i) Determine whether the relation R is reflexive, irreflexive, symmetric,antisymmetric, asymmetric, or transitive. Give a counterexample or anexplanation if your answer is “No”.
There are 6 towns {A, B, C, D, E, F} with the following one way street relation {(A, B), (A, C), (B, D), (C, B), (D, C), (D, F), (E, C), (E, F)}. Show all pairs of distinct towns that are reachable from one another in both directions.
Consider the relations R = {(1,5), (2, 2), (3, 4), (5, 2)}, S = {(2,4), (3, 4), (3, 1), (5, 5)}, T = {(1,4), (3, 5), (4, 1)} on the set A = {1,2,3, 4, 5}. Find (a) SoR = (b) RoT = (c) ToS = (d) Ro R= (e) SoS = (() ТоТ%—
4. Let Let A= {2,4} and B={1,3,5} and define relations U, v, and W from A to B as follows. For all (x, y) e AXB, (x, y) EU means that y-x> 2 (x, y) eV means that アー1= W ={(2,5),(4,1),(2,3)} a. Draw arrow diagrams for U, V, and W b. Indicate whether any of the relations U, V, and W are functions. Explain your answers
5. Let R1 and R2 be the relations on {1,2,3,4} given by R = {(1,1), (1,2), (3,4), (4,2)} R2 = {(1,1), (2,1), (3,1), (4,4), (2,2), (3,3)} a) List the elements of R, o R, and R, o R, . b) Is R2 reflexive? Justify your answer. c) Is R, o R, transitive? Justify your answer. d) Find R2-R1.
Draw a directed graph (digraph) for the relation on {1,2,3,4} {(1,1), (1,4), (2,2), (3,3), (4,1)
Let A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P),(R, P), (S, Q), (S, R)}. Find B^2 (pairs of towns that are connected by two streets). Find B^3(pairs of towns that are connected by three streets). You must use directed graph to findthe answer.
What is the composite of the relations R and S, where R is the relation from {1, 2, 3} to {1, 2, 3, 4} with R = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 4)} and S is the relation from {1, 2, 3, 4} to {0, 1, 2} with S = {(1, 0), (2, 0), (3, 1), (3, 2), (4, 1)}?
Let U={-5,-4,-3,-2,-1,0,1,2,3,4,5}, A={0,1,2,3,4,5} and B={-4,-2,0,2,4}. Perform the indicated set operation: B'∩(A-B).