Question

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.

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

Homework Answers

Answer #1

since R is reflexive,symmetric and transitive R is an equivalence relation on Z.

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
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.
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.
Let R be the relation of congruence mod4 on Z: aRb if a-b= 4k, for some...
Let R be the relation of congruence mod4 on Z: aRb if a-b= 4k, for some k E Z. (b) What integers are in the equivalence class of 31? (c) How many distinct equivalence classes are there? What are they? Repeat the above for congruence mod 5.
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)
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,
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.
Suppose we define the relation R on the set of all people by the rule "a...
Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b." Is this relation reflexive?  Is is symmetric?   Is it transitive?   Is it an equivalence relation? Briefly but clearly justify your answers.
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)].
Consider the relation on the real numbers R. a ~ b if (a−b) ∈ Z. (Z...
Consider the relation on the real numbers R. a ~ b if (a−b) ∈ Z. (Z is the whole integers.) 1) Give two real numbers that are in the same equivalence class. 2) Give two real numbers that are not in the same equivalence class. 3) Prove that this relation is an equivalence relation.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT