# prove

• Feb 17th 2008, 12:44 PM
rodemich
prove
im lookin for some help on this prove...

Let U be a set and let A and B be subsets of U.
Prove (A\B) compliement = A compliment Union B

thanks
• Feb 17th 2008, 01:07 PM
Plato
$\left( {A\backslash B} \right)^c = \left( {A \cap B^c } \right)^c$
You should be able to carry it forward and finish.
• Feb 17th 2008, 04:51 PM
rodemich
would anybody be able to help work this out? I'm new at this, and the more info that could be included, the more it would help me out. thanks, i appreciate it
• Feb 17th 2008, 07:28 PM
topsquark
Quote:

Originally Posted by rodemich
would anybody be able to help work this out? I'm new at this, and the more info that could be included, the more it would help me out. thanks, i appreciate it

Show us what you can do with Plato's hint.

-Dan
• Feb 17th 2008, 08:02 PM
rodemich
well i know to prove the equivalence, i need to prove that the statement is true both ways, right?
• Feb 17th 2008, 08:12 PM
rodemich
so i gotta prove both

(A/B)* is a subset of A* U B

and

A* U B is a subset of (A/B)*
• Feb 17th 2008, 08:14 PM
topsquark
Quote:

Originally Posted by rodemich
well i know to prove the equivalence, i need to prove that the statement is true both ways, right?

I don't understand. If you can show $\left ( A \backslash B \right ) ^c$ can be transformed into $\left ( A \cap B ^c \right )^c$ then you are done.

-Dan
• Feb 17th 2008, 08:15 PM
Jhevon
Quote:

Originally Posted by rodemich
so i gotta prove both

(A/B)* is a subset of A* U B

and

A* U B is a subset of (A/B)*

that's the hard way. continue from where Plato left off, and apply one of DeMorgan's laws

(do you know DeMorgan's laws?)
• Feb 17th 2008, 08:42 PM
rodemich
im fairly familiar with De Morgans Laws, but not enough to use it on my own yet
• Feb 17th 2008, 08:45 PM
Jhevon
Quote:

Originally Posted by rodemich
im fairly familiar with De Morgans Laws, but not enough to use it on my own yet

if $X$ and $Y$ are sets, what would DeMorgan's laws transform $(X \cap Y)^c$ into?