Consider the languages below. For each, make a conjecture whether or not it is regular. Then
prove your conjecture.
(a) $L=$ {$a^nb^la^k:n+k+l \gt 5$}
(b) $L=$ {$a^nb^la^k:n \gt 5,l> 3,k\leq l$}
(c) $L=$ {$a^nb^l:n/l$ is an integer}
(d) $L=$ {$a^nb^l:n+l$ is a prime number}
(e) $L=$ {$a^nb^l:n\leq l\leq 2n$}
(f) $L=$ {$a^nb^l:n\geq 100,l\leq 100$}
(g) $L=$ {$a^nb^l:|n-l|=2$}