Question

Suppose that R and S are equivalence relations on a set A. Prove that \( R \cap S \) is an equivalence relation on A

Answer 1

How far have you gotten so far in proving it's an equivalence relation?

Answer 2

ummmm hmmm well like in my book there were like a few proofs but i didnt follow any

Answer 3

Well, we need to show three things.
1. Reflexivity
2. Symmetry
3. Transitivity

Let's start with reflexivity. Suppose \(x,y,z\in A\). Since \(R,S\) are equivalence relations. \((x,x)\in R\) and \((x,x)\in S\).Therefore, \((x,x)\in R\cap S\).

Answer 4

ohhhh that stufff

Answer 5

okkkkkk I am fine with that stuff

Answer 6

uh oh my papres r flying all over brb

Answer 7

alrrighhtttyyy Thanks :DDDDDDD

Answer 8

So can you finish the other parts up from here then?

Answer 9

ya i hope sooooooooooooooooooooooo

Answer 10

Thanks :DDDDDD

Answer 11

You're welcome. Give me a holler if you still need some help.

Answer 12

hahahah u know me i will :DDD
like i know this stuff so i just wanna work it through on my own first