# Math Help - prove

1. ## 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

2. $\left( {A\backslash B} \right)^c = \left( {A \cap B^c } \right)^c$
You should be able to carry it forward and finish.

3. 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

4. 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

5. well i know to prove the equivalence, i need to prove that the statement is true both ways, right?

6. so i gotta prove both

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

and

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

7. 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

8. 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?)

9. im fairly familiar with De Morgans Laws, but not enough to use it on my own yet

10. 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?