$1\mathrm{.}54$ Consider the language $F=\{\begin{array}{c}{a}^i{b}^j{c}^k|i\\ j\\ k0\end{array}$ 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 pumping length $p$ and demonstrate that $F$ satisfies the three

conditions of the pumping lemma for this value of $p.$