Induction proof help need. Please explain the thought process with your answer.

Problem 1 (30pt) Consider a set S of pairs of integers. The set is defined as follows. Pair (0,0) is in S, i.e. (0,0) E S. If some pair (a, b) E S, then the following pairs are also in S: (a, b +1) E S, (a +1,b+1) ES and (a 2,b +1) E S. Prove (by induction) that for each pair (a, b) E S we have that a S 2b. Hint: observe that S is defined recursively, its first four elements are S (0,0), (0,1), (1, 1), (2, 1),...)