Q points$).$ Consider the following language over $=\{a,b,c\}$ :

$F=\{a^i{b}^j{c}^k|i,j,k0$ and $ifi=1$ 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 $p.$

$($c$)$ Explain why parts $($a$)$ and $($b$)$ do not contradict the pumping lemma.

Q points$).$ Consider the following language over $=\{a,b,c\}$ :

$F=\{a^i{b}^j{c}^k|i,j,k0$ and $ifi=1$ 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 $p.$

$($c$)$ Explain why parts $($a$)$ and $($b$)$ do not contradict the pumping lemma.

Q points$).$ Consider the following language over $=\{a,b,c\}$ :

$F=\{a^i{b}^j{c}^k|i,j,k0$ and $ifi=1$ 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 $p.$

$($c$)$ Explain why parts $($a$)$ and $($b$)$ do not contradict the pumping lemma.