Questions about equivalance relations and equivalance classes. . .

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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.

Re: Questions about equivalance relations and equivalance classes. . .

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**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.

Re: Questions about equivalance relations and equivalance classes. . .

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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.