Question

All strings of the form a^mb^n where m is even and n is odd. Question is: List the first 10 strings of the language in question above in canonical order

Answer 1

From the question:

Language L = {a^m bⁿ} where m is even and n is odd.

First 10 strings of the language canonical order:

1) m=0 and n=1 => a⁰ b¹ = b

2) m=2 and n=1 => a² b¹ = aab

3) m=0 and n=3 => a⁰ b³ = bbb

4) m=4 and n=1 => a⁴ b¹ = aaaab

5) m=2 and n=3 => a² b³ = aabbb

6) m=0 and n=5 => a⁰ b⁵ = bbbbb

7) m=6 and n=1 => a⁶ b¹ = aaaaaab

8) m=4 and n=3 => a⁴ b³ = aaaabbb

9) m=2 and n=5 => a² b⁵ = aabbbbb

10) m=0 and n=7 => a⁰ b⁷ = bbbbbbb

Therefore the first 10 strings of the language L in canonical order = {b, aab, bbb, aaaab, aabbb, bbbbb, aaaaaab, aaaabbb, aabbbbb, bbbbbbb}