# Distributive Laws for sets

• Oct 12th 2009, 04:12 PM
minkyboodle
Distributive Laws for sets
One of the following distributive laws for sets is true. Which one is and what is the proof?

A$\displaystyle \cap$(B$\displaystyle \oplus$C)=(A$\displaystyle \cap$B)$\displaystyle \oplus$(A$\displaystyle \cap$C)

A$\displaystyle \cup$(B$\displaystyle \oplus$C)=(A$\displaystyle \cup$B)$\displaystyle \oplus$(A$\displaystyle \cup$C)
• Oct 12th 2009, 04:55 PM
Plato
I think all you need to notice is that
$\displaystyle B \oplus C = \left( {B \cap C^c } \right) \cup \left( {B^c \cap C} \right)$
• Oct 12th 2009, 05:01 PM
minkyboodle
so, which one is right?
• Oct 12th 2009, 05:22 PM
Plato
Quote:

Originally Posted by minkyboodle
so, which one is right?

That is for you to work out.
Why do you expect to be handed the answer?
Is this not a question given to you after all?
• Oct 12th 2009, 06:47 PM
HallsofIvy
This makes 6 homework problems you have posted without any sign of an attempt to do the problems yourself. You can't learn by having other people do your work for you!