Need to check proof of De Morgan's law

[issacnewton]

Homework Statement

Hi

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

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

Homework Equations

Proof:

The Attempt at a Solution

$\mbox{let}\ x\in A\cap B\ \mbox{be arbitrary}$
$\Rightarrow x \in A\ \mbox{and}\ x \in B$
$\Rightarrow x \in A\ \mbox{and}\ x \notin B^{c}$
$\Rightarrow x \in A\ \mbox{and}\ x \notin A\setminus B$
$\Rightarrow x \in A\setminus (A\setminus B)$

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

Thanks

 

[ystael]

This is correct so far as it goes, yes.