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

<br /> A\cap B=A\setminus(A\setminus B)<br />

Homework Equations

Proof:

The Attempt at a Solution

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

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.