Question

Define a relation R on Z by aRb if and only if |a| = |b|. a)...

Define a relation R on Z by aRb if and only if |a| = |b|.

a) Prove R is an equivalence relation

b) Compute [0] and [n] for n in Z with n different than 0.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Define a relation on Z as aRb if 3 | (2a − 5b). Is R an...
Define a relation on Z as aRb if 3 | (2a − 5b). Is R an equivalence relation? Justify your answer.
Let R be the relation on Z defined by: For any a, b ∈ Z ,...
Let R be the relation on Z defined by: For any a, b ∈ Z , aRb if and only if 4 | (a + 3b). (a) Prove that R is an equivalence relation. (b) Prove that for all integers a and b, aRb if and only if a ≡ b (mod 4)
Define the relation τ on Z by aτ b if and only if there exists x...
Define the relation τ on Z by aτ b if and only if there exists x ∈ {1,4,16} such that ax ≡ b (mod 63). (a) Prove that τ is an equivalence relation. (b) Prove that there exists an integer n with 1 ≤ n ≤ 62 such that the equivalence class of n is{m ∈ Z | m ≡ n (mod 63)}.
(9 marks) Define the relation τ on Z by a τ b if and only if...
Define the relation τ on Z by a τ b if and only if there exists x ∈ {1, 4, 16} such that ax ≡ b (mod 63). (a) Prove that τ is an equivalence relation. (b) Prove that there exists an integer n with 1 ≤ n ≤ 62 such that the equivalence class of n is {m ∈ Z | m ≡ n (mod 63)}.
A relation R is defined on Z by aRb if 7x − 5y is even. Show...
A relation R is defined on Z by aRb if 7x − 5y is even. Show that R is an equivalence relation.
(Please Show all work)A relation R is defined on Z by aRb if 7x−5y is even....
(Please Show all work)A relation R is defined on Z by aRb if 7x−5y is even. Show that R is an equivalence relation.
A relation R is defined on Z by aRb if |a−b| ≤ 2. Which of the...
A relation R is defined on Z by aRb if |a−b| ≤ 2. Which of the properties reflexive, symmetric and transitive does the relation R possess? Explain why If R does not possess one of these properties,
13. Let R be a relation on Z × Z be defined as (a, b) R...
13. Let R be a relation on Z × Z be defined as (a, b) R (c, d) if and only if a + d = b + c. a. Prove that R is an equivalence relation on Z × Z. b. Determine [(2, 3)].
A relation R is called atransitive if aRb and bRc implies cRa. Show that R is...
A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and atransitive if and only if R is an equivalence relation.
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT