1. The problem statement, all variables and given/known data I'm asked to say whether the set Q,+,. is a field. To be a field it must respect 8 conditions. And one of them is that there exists a unique element -x in Q such that x+(-x)=0 for all x in Q. I realize I have to prove the existence of -x but also its uniqueness. For the existence I don't know how could I approach it. For the uniqueness I'm sure that I could do it by absurd. That is by suposing that there exist more than one element -x that satisfies the same property and fall into a contradiction. Can you get me started or help to get started for showing the existence? Thank you!