Please edit if it is off-topic as I don't know where to put it.
Let be the subset of ℤ × ℤ defined as:
Basis step:
$• (0, 0) ∈ $
Recursive step: if (, ) ∈ , then:
$• (, + 1) ∈ $
$• ( + 1, + 1) ∈ $
$• ( + 2, + 1) ∈ $
a. List 5 elements of ℤ × ℤ that are in .
b. List 5 elements of ℤ × ℤ that are not in .
c. Make a conjecture about the elements of ; that is, formulate a statement that is true for every (,) in . For example: for every (, ) in , ≥ 0 and ≥ 0.
My attempt->
a) $(0,1)$,$(1,1)$,$(2,1)$,$(3,2)$,$(3,3)$
b)$(1,0)$,$(2,0)$,$(3,0)$,$(4,0)$,$(5,0)$
c) I don't know how to do this
Please verify mine and correct if there was any worng