I'm studying for a mathematics class and have been struggling with the following proof
$$A-(A-B) = A ∩ B$$
I know we have to use the following rule $A-B = A ∩ B^c$ which is set $B$'s complement known as the set difference law.
Do I have everything necessary to solve this prove? Is this proof possible because using the complements won't seem to result in the $A ∩ B$ that is required.
Thank you guys I gained some confidence and done the proof this is what I got
A-B = A ∩ B^(c) - Set Difference Law
A- (A ∩ B^(c)) = A ∩ B
A- (A ∩ B^(c)) = (A ∩ (A ∩ B^(c)) ^c) - Set Difference Law
(A ∩ (A ∩ B^(c)) ^c) = A ∩ B - double Complement Law
(A ∩ (A ∩ B)) = A ∩ B
A ∩ A = A - Idempotent Laws (Can I do this?)
A ∩ B = A ∩ B
I think this proof is close to correct. I was confused with the last part but it seems to check out.
Edit 2- Nevermind Looks like my proof was all wrong. Is there any way to redeem my current proof?