Math Help - Set and subets of a universal set

1. Set and subets of a universal set

Alright here is the question

Let A, B, C be subsets of a universal set. Show

A-(B intersection C)= (A-B) union (A-C)

Ok my thoughts, I understand how logically this is true, If you subtract the like terms of B and C from set A it is the same as taking a the union of both.
For instance if A= {1,3} and B= {2,4,7} and C= {3,4,6}. Then A-(B inter C) will equal {-4}+{1,3}. Also i know that A-B union A-C equals the same thing.
Can someone help tell me how to put it in proof form? I know whats going on just not how to say it.

2. Originally Posted by j5sawicki
Let A, B, C be subsets of a universal set. Show
A-(B intersection C)= (A-B) union (A-C)
$A\backslash \left( {B \cap C} \right) = A \cap \left( {B \cap C} \right)^c = A \cap \left( {B^c \cup C^c } \right) = \left( {A \cap B^c } \right) \cup \left( {A \cap C^c } \right)$

3. Thank you

Really thats all i have to say this may be a stupid question but what does the c in the corner mean

4. Originally Posted by j5sawicki
Really thats all i have to say this may be a stupid question but what does the c in the corner mean
$A^c$ means A-complement. That is to say the set of all members of set $U$ not in set $A$, as a generalization.

5. are you actually being graded on rigorous proofs? because if you are then you probably need more than what Plato said if you want more credit, for instance, you'd probably need to prove the compliments identity he uses

but if this is just a "show why" problem or something, you'll be good with what he said