Question

4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an...

4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an equivalence relation on the set of real numbers, where Q denotes the set of rational numbers.

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
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.
Recall that Q+ denotes the set of positive rational numbers. Prove that Q+ x Q+ (Q+...
Recall that Q+ denotes the set of positive rational numbers. Prove that Q+ x Q+ (Q+ cross Q+) is countably infinite.
1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove...
1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove R∪(S∩T) = (R∪S)∩(R∪T). 4.Consider the relation R={(x,y)∈R×R||x−y|≤1} on Z. Show that this relation is reflexive and symmetric but not transitive.
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.
I have a discrete math question. let R be a relation on the set of all...
I have a discrete math question. let R be a relation on the set of all real numbers given by cry if and only if x-y = 2piK for some integer K. prove that R is an equivalence relation.
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...
6. Define S={q∈Q:−√3< q <√3}, where Q denotes the rational numbers. Prove that S can not...
6. Define S={q∈Q:−√3< q <√3}, where Q denotes the rational numbers. Prove that S can not be the set of subsequential limits of any sequence (sn) of reals. Please be very verbose. I already have the answer to this question as a contradiction. It is okay if you use a contradiction, however please explain thoroughly.
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.
Let R be a relation on set RxR of ordered pairs of real numbers such that...
Let R be a relation on set RxR of ordered pairs of real numbers such that (a,b)R(c,d) if a+d=b+c. Prove that R is an equivalence relation and find equivalence class [(0,b)]R
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT