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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) $L=$ {$a^nb^l:|n-l|=2$}

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