2009-9 min or max

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.
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2009-9 min or max, 4.0 out of 5 based on 4 ratings