$3)[4$ x $2=8$ points$]$

Regular expressions: Let $\backslash$Sigma $=\{$a $,$ b $$ be defined as the alphabet. Write down regular

expressions for $($a$)$ through $($d$).$ Further, write down some of the strings which fall under

each of the below four languages:

$($a$)$ L$1$ is a language which defines all strings ending in the string $$ab$.$

$($b$)$ L$2$ is a language which defines all strings containing $$aba$$

$($c$)$ L $3$ is a language which defines all strings not ending in the string $$aba$$

$($d$)$ L$4$ is a language which defines all strings beginning with $$aa$$ and ending in $$bb$$