# Questions about equivalance relations and equivalance classes. . .

• Aug 31st 2011, 01:54 PM
Dakaa
Questions about equivalance relations and equivalance classes. . .
http://i54.tinypic.com/1z2q1dl.png

for the first question, can i assume the non-empty set A has more than one element, and say a = something and b = something to give example.
• Aug 31st 2011, 07:56 PM
FernandoRevilla
Re: Questions about equivalance relations and equivalance classes. . .
Quote:

Originally Posted by Dakaa
http://i54.tinypic.com/1z2q1dl.png

for the first question, can i assume the non-empty set A has more than one element, and say a = something and b = something to give example.

No, you can't. Choose for example $\displaystyle A=\{0\}$ . A little help: Reflexive For all $\displaystyle x\in\mathbb{Z}$ we have $\displaystyle x-x=0$ . But $\displaystyle 0\in A$ because being $\displaystyle A\neq \emptyset$ , choosing $\displaystyle a\in A$ we have $\displaystyle a-a=0\in A$ . Conclusion: $\displaystyle xRx$ .

Try the rest.
• Sep 4th 2011, 07:13 PM
Dakaa
Re: Questions about equivalance relations and equivalance classes. . .
Quote:

Originally Posted by FernandoRevilla
No, you can't. Choose for example $\displaystyle A=\{0\}$ . A little help: Reflexive For all $\displaystyle x\in\mathbb{Z}$ we have $\displaystyle x-x=0$ . But $\displaystyle 0\in A$ because being $\displaystyle A\neq \emptyset$ , choosing $\displaystyle a\in A$ we have $\displaystyle a-a=0\in A$ . Conclusion: $\displaystyle xRx$ .

Try the rest.

Yup, did the rest, now moving on to question 2.