# Question: let b z z be the set of...

###### Question details

Let B ⊆ Z × Z be the set of ordered pairs defined recursively by:

(0, 0) ∈ B and If (a, b) ∈ B then, (a, b + 1) ∈ B,(a + 1, b + 1) ∈ B, and (a + 2, b + 1) ∈ B

Prove that for every (a, b) ∈ B we have a ≤ 2b.