1. The problem statement, all variables and given/known data Prove -(-x) = x. 2. Relevant equations A2: x + y = y + x [additive commutativity] A5: x + (-x) = 0 M3: x(yz) = (xy)z [multiplicative associativity] M4: x (1) = x Lemma: (-1)(-1) = 1 Theorem c: (-1)x = -x 3. The attempt at a solution -(-x) = (-1)[(-1)x] by Theorem c = [(-1)(-1)]x by M3 = (1)x by lemma = x by M4 Q.E.D. This is what my approach was; however, the solution in the back of the book was something like this: From A5 we have x + (-x) = 0. Then (-x) + x = 0 by A2. Hence x = - (-x) by the uniqueness of -(-x) in A5. Q.E.D. Is my approach a viable proof? I thought I was starting to understand this, but when I see the solution it completely throws me off. Additionally, the proof given by the book makes no sense to me. I have no intuition for this.