![Question 5 (4 points each Let R be the relation on the set of ordered pairs of positive integers such that (a, b), (c, d)) E R if and only if ad bc. (1) Show that R is an equivalence relation (2) What is the equivalence class of of (1,2), i.e. (1,2)]?](http://img.homeworklib.com/questions/bf01ef80-8337-11eb-90f1-89eb2018f11c.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
Let R be the relation on the set of ordered pairs of positive integers such that...
Prove that the following relation R is an equivalence relation on the set of ordered pairs...
Prove that the following relation R is an equivalence
relation on the set of ordered pairs of real numbers. Describe the
equivalence classes of R. (x, y)R(w, z)
y-x2 = z-w2
*ESPECIALLY PART D PLEASE 111111 1. Let R be a relation on RxR defined by (a,b)R(c,d)...
*ESPECIALLY PART D PLEASE
111111 1. Let R be a relation on RxR defined by (a,b)R(c,d) if and only if a - b = c-d DIDUD a) (5 points) Prove that is an equivalence relation on RxR. b) (5 points) Describe all ordered pairs in the equivalence class of (0,0) c) (5 points) Describe all ordered pairs in the equivalence class of (3,1) d) (5 points) Describe the partition of Rx Rassociated with R.
3. Let the relation R be defined on the set R by a Rb if a...
3. Let the relation R be defined on the set R by a Rb if a -b is an integer. Is R and equivalence relation? If yes, provide a proof. Consider the equivalence relation in #3. a. What is the equivalence class of 3 for this relation? 1 b. What is the equivalence class of for this relation? 2
(14) Let R be a relation on the integers defined by m R n if and...
(14) Let R be a relation on the integers defined by m R n if and only if m+m2 n+ n2(mod 5). Show that R is an equivalence relation and determine all the equivalence classes.
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R...
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R 3 c) R 4 d) R 5 Consider the same relation R as above. List all walks in R staring from node 3 that correspond to the edges in a) R 2 b) R 3
probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R =...
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1,...
discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) Î R if and only if a) a = b b) a + b = 4 c) a > b d) a|b //6th edition ((a), (b), (c), and (d) of Exercise 1, Page 527.) 2. a) List all the ordered pairs in the relation R = {(a, b) |a divides b}...
Show that the relation R on the set of differentiable functions from R to R consisting of all pai...
Show that the relation R on the set of differentiable functions from R to R consisting of all pairs of functions f, g such that f(x) -() is an equivalence relation. What functions are in the equivalence class of f(x) ??
Show that the relation R on the set of differentiable functions from R to R consisting of all pairs of functions f, g such that f(x) -() is an equivalence relation. What functions are in the equivalence class of...
Question 8 Let R be relation on a set A. 1. When is R said to...
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3...
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R b if
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R...
Prove that the following relation R is an equivalence
relation on the set of ordered pairs of real numbers. Describe the
equivalence classes of R. (x, y)R(w, z)
y-x2 = z-w2
*ESPECIALLY PART D PLEASE
111111 1. Let R be a relation on RxR defined by (a,b)R(c,d) if and only if a - b = c-d DIDUD a) (5 points) Prove that is an equivalence relation on RxR. b) (5 points) Describe all ordered pairs in the equivalence class of (0,0) c) (5 points) Describe all ordered pairs in the equivalence class of (3,1) d) (5 points) Describe the partition of Rx Rassociated with R.
3. Let the relation R be defined on the set R by a Rb if a -b is an integer. Is R and equivalence relation? If yes, provide a proof. Consider the equivalence relation in #3. a. What is the equivalence class of 3 for this relation? 1 b. What is the equivalence class of for this relation? 2
(14) Let R be a relation on the integers defined by m R n if and only if m+m2 n+ n2(mod 5). Show that R is an equivalence relation and determine all the equivalence classes.
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
Show that the relation R on the set of differentiable functions from R to R consisting of all pairs of functions f, g such that f(x) -() is an equivalence relation. What functions are in the equivalence class of f(x) ??
Show that the relation R on the set of differentiable functions from R to R consisting of all pairs of functions f, g such that f(x) -() is an equivalence relation. What functions are in the equivalence class of...
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R b if
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R...
Most questions answered within 3 hours.
-
Suppose a quiz contains 20 true/false questions. You
know the correct answer to the first 10...
asked 24 minutes ago -
Is depression the cause or the effect of a stressful
situation? Explain.
12) How do learning...
asked 1 hour ago -
Critically discuss whether the Bretton Woods System has been
based on Keynesian principles. Please give me...
asked 1 hour ago -
An ammeter with a scale ranging from 0 to 15mA has a resistance
of 5Omega. How...
asked 2 hours ago -
def blur(img: Image) -> Image:
"""Blur Image, img, based on the given pixel_size
Hints:
- For...
asked 2 hours ago -
a
carboxylic acid reacting with a strong base will form what
ion
asked 4 hours ago -
which value if any in each pair corresponds to a
faster reaction k=18.k=137
asked 4 hours ago -
Bus lines can be separated into two generic types, dedicated and
multiplexed.
i. What is the...
asked 6 hours ago -
This is 'Branding' course which is part of marketing.
1. As a brand manager of Nudie...
asked 6 hours ago -
You are considering the purchase of a new stock. The stock is
forecasted to pay a...
asked 6 hours ago -
vector a has componets Ax and Ay, and makes an angle theta with
the y-axis. Select...
asked 7 hours ago -
What were the problems of the american frontier after 1763 and how
did the British address...
asked 8 hours ago