text: 1. ## 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.
  
  2. ## Re: Questions about equivalance relations and equivalance classes. . .
  
  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.
  
  3. ## Re: Questions about equivalance relations and equivalance classes. . .
  
  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.
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