Discrete Mathamatics Proving

1. Jan 30, 2012

geforce

Prove that (A n B) - C = (A - C) n (B - C).

n = intersect
≠ε = not a member

I got the first one by doing:
(xεA ^xεB) ^X≠εC ( by identity law and compliment law)

where would I go on from now?

2. Jan 30, 2012

issacnewton

so basically you have to prove the equality of sets. forward way is to let $x\in(A\cap B)\setminus C$ be arbitrary. Then as you have shown

$$x\in A\;x\in B\;\; x\notin C$$

which means that x is A and not in C AND x is in B and not in C. So just combine that to arrive at the right side. Then proceed to the reverse direction.

3. Jan 30, 2012

geforce

What do you mean as in "(A∩B)∖C"to be arbitrary and I have to show how it goes from (A∩B) -C to (A-C) ∩ (B-C)

4. Jan 30, 2012

geforce

?....

5. Jan 30, 2012

issacnewton

when you have to prove that two sets are equal you have to prove that

$$A\subseteq B\mbox{ and }B\subseteq A$$

So to prove $A\subseteq B$ you take arbitrary member of A and then prove that
its also member of B. And similar proof for proving $B\subseteq A$