Proving identities without Venn diagrams

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December 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.
December 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)

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

Quote:

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.
December 14th 2009, 07:20 AM
Plato

Quote:

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.
December 14th 2009, 07:21 AM
jnick

Quote:

Originally Posted by Plato

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

Perfect. Thanks for the help!

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