$8.$ Provide NFAs accepting the following languages over the alphabet $\backslash$Sigma $=\{$a$,$b$\}.$

Note: For w in $\backslash$Sigma $,\backslash$sigma in $\backslash$Sigma $,$ we use n$\backslash$sigma $($w$)$ to mean the number of letters $\backslash$sigma in w$.$

A$)$ LA $=\{$w in $\backslash$Sigma $$ : w contains the substring ababa$\}$

B$)$ LB $=\{$w in $\backslash$Sigma $$: na$($w$)$ mod $2=1$ or nb$($w$)$ mod $3=2\}$

C$)$ LC $=\{$w in $\backslash$Sigma $$ : w starts and ends with the same letter$\}$

A proof of correctness is not required. No points will be awarded for overly complicated automata. In other words, you must use non$-$determinism.