Consider the language F = {aⁱb^jc^k | i, j, k 0 and if i = 1 then j = k}.

a. Show that F is not regular

b. Show that F acts like a regular language in the pumping lemma. In other words, give a pump length p and demonstrate that F satisfies the three conditions of the pumping lemme for this value of p.

c. Explain why parts a and b don't contradict pumping lemma.