Question

Problem 13.5. Consider a “square” S = {(x, y) : x, y ∈ {−2, −1, 0,...

Problem 13.5. Consider a “square” S = {(x, y) : x, y ∈ {−2, −1, 0, 1, 2}}. (a) Let (x, y) ∼ (x 0 , y0 ) iff |x| + |y| = |x 0 | + |y 0 |. It is an equivalence relation on S. (You don’t need to prove it.) Write the elements of S/ ∼. (b) Let (x, y) ∼ (x 0 , y0 ) iff • x and x 0 have the same sign (both positive, both negative, or both 0), and • y and y 0 have the same sign (defined as above). It is an equivalence relation on S. (You don’t need to prove it.) Write the elements of S/ ∼.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each of the following, prove that the relation is an equivalence relation. Then give the...
For each of the following, prove that the relation is an equivalence relation. Then give the information about the equivalence classes, as specified. a) The relation ∼ on R defined by x ∼ y iff x = y or xy = 2. Explicitly find the equivalence classes [2], [3], [−4/5 ], and [0] b) The relation ∼ on R+ × R+ defined by (x, y) ∼ (u, v) iff x2v = u2y. Explicitly find the equivalence classes [(5, 2)] and...
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2...
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2 + b^2. a) Prove S in an equivalence relation b) compute [(0,0)], [(1,2)], and [(-3,4)]. c) Draw a picture in R^2 representing these three equivalence classes.
Write vectors in R2 as (x,y). Define the relation on R2 by writing (x1,y1) ∼ (x2,y2)...
Write vectors in R2 as (x,y). Define the relation on R2 by writing (x1,y1) ∼ (x2,y2) iff y1 − sin x1 = y2 − sin x2 . Prove that ∼ is an equivalence relation. Find the classes [(0, 0)], [(2, π/2)] and draw them on the plane. Describe the sets which are the equivalence classes for this relation.
Let R = {(x, y) | x − y is an integer} be a relation on...
Let R = {(x, y) | x − y is an integer} be a relation on the set Q of rational numbers. a) [6 marks] Prove that R is an equivalence relation on Q. b) [2 marks] What is the equivalence class of 0? c) [2 marks] What is the equivalence class of 1/2?
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a)...
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a) Explain why R is not an equivalence relation. b) Explain why S is not an equivalence relation. c) Find S ◦ R. d) Show that S ◦ R is an equivalence relation. e) What are the equivalence classes of S ◦ R?
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. I need to prove that: a) R is an equivalence relation. (which I have) b) The equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq I...
Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)^2 = x^2 +...
Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)^2 = x^2 + y^2, and let (x0, y0, z0) be a point in their intersection. Show that the surfaces are tangent at this point, that is, show that they have a common tangent plane at (x0, y0, z0).
Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation on S for reflexivity, symmetry, antisymmetry, and...
Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation on S for reflexivity, symmetry, antisymmetry, and transitivity. xρy if and only if x+y = 8. Is ρ an equivalence relation? If we change the relation to x ρ y if and only if x+y 6 8 how will the cardinality of ρ change? Give a detailed explanation. 2. draw the Hasse diagram for the partial ordering “x divides y” on the set {24,3,4,12,96,15,21,36}. Name any least elements, minimal elements, greatest...
Let X = [0, 1) and Y = (0, 2). a. Define a 1-1 function from...
Let X = [0, 1) and Y = (0, 2). a. Define a 1-1 function from X to Y that is NOT onto Y . Prove that it is not onto Y . b. Define a 1-1 function from Y to X that is NOT onto X. Prove that it is not onto X. c. How can we use this to prove that [0, 1) ∼ (0, 2)?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT