- #1

issacnewton

- 1,020

- 35

## Homework Statement

Hi

I have done the proof, just need to check it. I wanted to prove that

[itex]

A\cap B=A\setminus(A\setminus B)

[/itex]

## Homework Equations

Proof:

## The Attempt at a Solution

[itex]

\mbox{let}\ x\in A\cap B\ \mbox{be arbitrary}

[/itex]

[itex]

\Rightarrow x \in A\ \mbox{and}\ x \in B

[/itex]

[itex]

\Rightarrow x \in A\ \mbox{and}\ x \notin B^{c}

[/itex]

[itex]

\Rightarrow x \in A\ \mbox{and}\ x \notin A\setminus B

[/itex]

[itex]

\Rightarrow x \in A\setminus (A\setminus B)

[/itex]

I know that I have to do reverse proof too. But is it ok so far ?

Thanks