# Formal boolean proofs.

1. Feb 2, 2010

### nahanksh

1. The problem statement, all variables and given/known data
Prove that
$$A \oplus B' \oplus C = (A \oplus B \oplus C)'$$

2. Relevant equations

3. The attempt at a solution
I tried to use $$A \oplus B' \oplus C$$ = ABC' + A'B'C' + A'BC + AB'C

But i am not sure how to proceed further from there...

Please could someone give me a little bit of help ?

2. Feb 2, 2010

### Synaesthesia

I would start with the right hand side - it can be rewritten with some laws.

3. Feb 2, 2010

### Synaesthesia

I'm sorry that was still vague. De Morgan's laws to be specific.
NOT (P OR Q) = (NOT P) AND (NOT Q)
NOT (P AND Q) = (NOT P) OR (NOT Q)

4. Feb 2, 2010

### Synaesthesia

I'm sorry that was still vague. De Morgan's laws to be specific.
NOT (P OR Q) = (NOT P) AND (NOT Q)
NOT (P AND Q) = (NOT P) OR (NOT Q)