do$!$ not use ai

Give a regular expression for each of the following languages. Show work and

explain why each regular expression is correct.

$($a$)\{$x in $\{0,1\}|$ bin$($x$)$ is a multiple of $2\}.$

$($b$)\{$x in $\{0,1\}|$ bin$($x$)$ is a multiple of $4\}.$

$($c$)\{$x in $\{0,1\}|$ bin$($x$)$ is a multiple of $3\}.$