∑∗
a, b
CONCAT
a. ODDnotAB ⊆ ∑∗
b. 𝑎, 𝑏 ∈ ODDnotAB
c.
If 𝑤 ∈ ODDnotAB and ends with an a, then CONCAT(w,aa) ∈ ODDnotAB
If 𝑤 ∈ ODDnotAB and ends with a b, then CONCAT(w,aa), CONCAT(w,bb), CONCAT(w,ba) ∈
ODDnotAB
If 𝑤 ∈ ODDnotAB and begins with an a, then CONCAT(bb,w), CONCAT(aa,w), CONCAT(ba,w) ∈
ODDnotAB
If 𝑤 ∈ ODDnotAB and begins with a b, then CONCAT(bb,w) ∈ ODDnotAB
1 ∈ 𝑃,
If 𝑥 ∈ 𝑃, then 𝑥 + 1 ∈ 𝑃
Nothing else is an element of P
If a subset of P contains 1 and also contains k+1 wherever it contains k, then the subset is in fact
equal to P
a, b
CONCAT
a. ODDnotAB ⊆ ∑∗
b. 𝑎, 𝑏 ∈ ODDnotAB
c.
If 𝑤 ∈ ODDnotAB and ends with an a, then CONCAT(w,aa) ∈ ODDnotAB
If 𝑤 ∈ ODDnotAB and ends with a b, then CONCAT(w,aa), CONCAT(w,bb), CONCAT(w,ba) ∈
ODDnotAB
If 𝑤 ∈ ODDnotAB and begins with an a, then CONCAT(bb,w), CONCAT(aa,w), CONCAT(ba,w) ∈
ODDnotAB
If 𝑤 ∈ ODDnotAB and begins with a b, then CONCAT(bb,w) ∈ ODDnotAB
1 ∈ 𝑃,
If 𝑥 ∈ 𝑃, then 𝑥 + 1 ∈ 𝑃
Nothing else is an element of P
If a subset of P contains 1 and also contains k+1 wherever it contains k, then the subset is in fact
equal to P
