Solution to Let R be an equivalence relation on Z, which has P={{±i}|i ∈ N} as its … - Sikademy
Author Image

Archangel Macsika

Let R be an equivalence relation on Z, which has P={{±i}|i ∈ N} as its collection of equivalence classes. Describe the equivalence relation R.

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

By definition(a,b)\in R if and only if a,b\in A for some A\in P.


Let us describe the equivalence relation R. It follows that for i\in\mathbb N we have that a,b\in\{\pm i\} if and only if |a|=|b|=i . Therefore, a,b\in\{\pm i\} for some i\in\mathbb N if and only if |a|=|b| .

               We conclude that (a,b)\in R if and only if |a|=|b|.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3475-qpid-2174