Q$1)$ Find NFA's for the following languages:

$L_1=\{2^n{1}^m{3}^k$:$n,m,k0\}on{\displaystyle \underset{?}{\overset{?}{}}}=\{1,2,3\}.$

$L_2=\{w\{a,b,c{\}}^{*}$: every appearance $ofainw$ before every appearance $ofcinw\}$

$L_3=\{w\{a,b,c,d{\}}^{*}$: number $of$ the last symbol $inw>1\}.$

$L_4=\{w\{0,1{\}}^{*}$:$w$ contains $101$ and $0110\}$

Q$2)$ Find FA's for the following languages:

$L_5=\{\begin{array}{ccc}{c}^{n}w\text{:}\text{w}\text{i}\text{n}& \{a,& b{\}}^{*}\text{:}n>0\\ ?\end{array}$

$Ifn=1$ then

$w$ ends $inbb$

else $ifn=2$ then

every $ais$ followed $byb$ and every $bis$ followed $bya$