Prove the following theorems.

1) Ifxis any number, then 0*x= 0.

2) Ifxis any number, there do not exist two numbersyandy'such thatx*y= 1 andx*y'= 1.

Use any of the following axioms to help prove the above theorems:

1) If each ofxandyis a number, thenx*yis a number.

2) If each ofxandyis a number, thenx*y = y*x.3) If each of

x,y, andzis a number, then (x*y)*z=x*(y*z).

4) There is a numberUsuch that ifxis any number, thenU*x = x.