Write inductive definitions of the following sets. Write each definition in all three styles (top-down, bottom-up, and rules of inference). Using your rules, show the derivation of some sample elements of each set.

1. {(n, 2n + 1) | n N}

2. {(n, n^2 ) | n N} where n^2 denotes n to the power of 2. Do not mention squaring in your rules. As a hint, remember the equation (n + 1)^2 = n^2 + 2n + 1.