1. The problem statement, all variables and given/known data Prove: If a and b are in N the [(1,1+a)] + [(1,1+b)] = [(1,1+a+b)] 2. Relevant equations Definition: We define + over Z as follows: if [(a,b)] and [(c,d)] are any two equivalence classes, we define [(a,b)] + [(c,d)] = [(a+c,b+d)]. 3. The attempt at a solution So the left hand is [(2,2+a+b)] since 2, a, b are all [tex]\in[/tex] N does this mean this is equivalent to [(1,1+a+b)]?