# Thread: Proving identities without Venn diagrams

1. ## Proving identities without Venn diagrams

Hi,

We are having some problems proving identities without Venn diagrams and wonder if anyone can help.

A\B = A\(AnB)

We can do this using Venn diagrams but have no idea how to do it without.

Thanks for any help.

2. Originally Posted by jnick
We are having some problems proving identities without Venn diagrams and wonder if anyone can help.
A\B = A\(AnB)
$A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)$

3. Originally Posted by Plato
$A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)$
Hi,

Thanks for the quick reply. Could you explain what $B^c$ means as we haven't seen this symbol before and can't find it in our text book(Rosen). Thanks again.

4. Originally Posted by jnick
Could you explain what $B^c$ means as we haven't seen this symbol before and can't find it in our text book(Rosen).
It means complement. Rosen uses $\overline{B}$ for the same notation.

5. Originally Posted by Plato
It means complement. Rosen uses $\overline{B}$ for the same notation.

Perfect. Thanks for the help!