Let R ⊂ Z+ × Z+ be the relation given by the following recursive definition.
1) (1, 1) ∈ R; and
2) For all (a, b) ∈ R, the three ordered pairs (a + 1, b), (a + 1, b + 1), and (a + 1, b + 2) are also in R
Prove that 2a > b for all (a, b) ∈ R.