Provide regular expressions for the following languages:

a$.$ The set of strings over the alphabet $\{$a$,$b$,$c$,\}$ containing at least one a and

least one b$.(5$ points$)$

b$.$ The set of strings over $\{0,1\}$ whose tenth symbol from the right end is $1.$

$(5$ points$)$

c$.$ The set of strings over $\{0,1\}$ not containing $101$ as a substring. $(5$ points$)$

$2.$ For every regular expression constructed in exercise $1$:

a$.$ Build an equivalent $\backslash$epsi $-$NFA. $(5$ points$)$

b$.$ Convert every $\backslash$epsi $-$NFA into a DFA by computing the epsilon$-$closures.

$(15$ points$)$