$8\backslash$times $2=16$ marks$)$

Suppose $\backslash$Sigma $=\{0,1\}.$ Show how to define the following languages over $\backslash$Sigma using only $,$

tokens $0$ and $1,$ and the operations of union, concatenation, and closure.

$($a$)$ All strings that begin with $0$ and end with $1.$

$($b$)$ All strings except the empty string.

$($c$)$ All strings that have at least two $1$s$.$

$($d$)$ All strings of even length.

$($e$)$ All strings such that all odd$-$numbered $($first$,$ third, fifth, $...)$ character positions

are $0$s$.$

$($f$)$ All strings that have $010$ as a suffix.

$($g$)$ All strings that have $010$ as a substring.

$($h$)$ All strings such that every run of $1$s is of even length; for example, $011000111100$

but not $0110010.$