Question

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 [(1, 4)]. For fixed values a, b ∈ R+, describe [(a, b)], both as a set and geometrically

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
4. Prove explicitly that congruence modulo 4 is an equivalence relation. Then list the equivalence classes....
4. Prove explicitly that congruence modulo 4 is an equivalence relation. Then list the equivalence classes. 5. Determine all of the equivalence classes for ZZ5
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on...
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on R2 In the previous problem: (1) Describe [(1,1)]∼. (That is formulate a statement P(x,y) such that [(1,1)]∼ = {(x,y) ∈ R2 | P(x,y)}.) (2) Describe [(a, b)]∼ for any given point (a, b). (3) Plot sets [(1,1)]∼ and [(0,0)]∼ in R2.
Determine the distance equivalence classes for the relation R is defined on ℤ by a R...
Determine the distance equivalence classes for the relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. I had to prove it was an equivalence relation as well, but that part was not hard. Just want to know if the logic and presentation is sound for the last part: 8.48) A relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. Prove that R...
In the following two problems, the equivalence classes refer to the equivalence classes under the equivalence...
In the following two problems, the equivalence classes refer to the equivalence classes under the equivalence relation: aRb iff n|(a-b) where n is a fixed integer. Suppose a, b, c, d are elements of the integers such that [a] = [b] and [c] = [d]. 1. Prove [a+d] = [b+c]. 2. Prove [ac] = [bd]
Consider the following relation on the set Z: xRy ? x2 + y is even. For...
Consider the following relation on the set Z: xRy ? x2 + y is even. For each question below, if your answer is "yes", then prove it, if your answer is "no", then show a counterexample. (i) Is R reflexive? (ii) Is R symmetric? (iii) Is R antisymmetric? (iv) Is R transitive? (v) Is R an equivalence relation? If it is, then describe the equivalence classes of R. How many equivalence classes are there?
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​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that...
Let ​R​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that ​R​^n​ is also an equivalence relation.
a) Let R be an equivalence relation defined on some set A. Prove using induction that...
a) Let R be an equivalence relation defined on some set A. Prove using induction that R^n is also an equivalence relation. Note: In order to prove transitivity, you may use the fact that R is transitive if and only if R^n⊆R for ever positive integer ​n b) Prove or disprove that a partial order cannot have a cycle.
Determine whether the given relation is an equivalence relation on {1,2,3,4,5}. If the relation is an...
Determine whether the given relation is an equivalence relation on {1,2,3,4,5}. If the relation is an equivalence relation, list the equivalence classes (x, y E {1, 2, 3, 4, 5}.) {(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4), (4,3)} If the relation above is not an equivalence relation, state that the relation is not an equivalence relation  and why. Example: "Not an equivalence relation. Relation is not symmetric" Remember to test all pairs in relation R
Prove that the relation R on the set of all people, defined by xRy if x...
Prove that the relation R on the set of all people, defined by xRy if x and y have the same first name is an equivalence relation.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT