Questions about equivalance relations and equivalance classes. . .

**Dakaa** · Aug 31st 2011, 01:54 PM

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.

**FernandoRevilla** · Aug 31st 2011, 07:56 PM

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 $A=\{0\}$ . A little help: Reflexive For all $x\in\mathbb{Z}$ we have $x-x=0$ . But $0\in A$ because being $A\neq \emptyset$ , choosing $a\in A$ we have $a-a=0\in A$ . Conclusion: $xRx$ .

Try the rest.

**Dakaa** · Sep 4th 2011, 07:13 PM

Originally Posted by FernandoRevilla

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

Try the rest.

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

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