# Proving identities without Venn diagrams

• Dec 14th 2009, 06:59 AM
jnick
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.
• Dec 14th 2009, 07:04 AM
Plato
Quote:

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

$\displaystyle A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)$
• Dec 14th 2009, 07:12 AM
jnick
Quote:

Originally Posted by Plato
$\displaystyle A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)$

Hi,

Thanks for the quick reply. Could you explain what $\displaystyle B^c$ means as we haven't seen this symbol before and can't find it in our text book(Rosen). Thanks again.
• Dec 14th 2009, 07:20 AM
Plato
Quote:

Originally Posted by jnick
Could you explain what $\displaystyle B^c$ means as we haven't seen this symbol before and can't find it in our text book(Rosen).

It means complement. Rosen uses $\displaystyle \overline{B}$ for the same notation.
• Dec 14th 2009, 07:21 AM
jnick
Quote:

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

Perfect. Thanks for the help!