Suppose that * is an associative and commutative binary operation on the set of rational numbers such that 

1. 0*0=0
2. (a+c)*(b+c)=(a*b)+c for all rational numbers a,b,c.

Prove that either

1. a*b=max(a,b) for all rational numbers a,b, or
2. a*b=min(a,b) for all rational number a,b.