Proving identities without Venn diagrams

**jnick** · December 14th 2009, 06:59 AM

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.

**Plato** · December 14th 2009, 07:04 AM

Originally Posted by jnick

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

$A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)$

**jnick** · December 14th 2009, 07:12 AM

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.

**Plato** · December 14th 2009, 07:20 AM

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.

**jnick** · December 14th 2009, 07:21 AM

Originally Posted by Plato

It means complement. Rosen uses $\overline{B}$ for the same notation.

Perfect. Thanks for the help!

Thread: Proving identities without Venn diagrams

LinkBack

Thread Tools

Display

Proving identities without Venn diagrams

Similar Math Help Forum Discussions

Venn diagrams

Venn Diagrams

Venn Diagrams

Venn Diagrams

A-B' and A'-B Venn Diagrams?

Search Tags