In Problems $1$ through $4,$ find CFG$\text{'}$s for the indicated languages over

S$=\{$a$,$ b$\}.$ When n appears as an exponent, it means n $=1,2,3...$

$1.$ All words that start with an a or are of the form a$^$nb$^$n$.$

$2.$ All words that start with a b or are of the form a$^$nb$^$n$.$

$3.$ All words that have an equal number of a$\text{'}$s and b$\text{'}$s or are of the form a$^$nb$^$n$.$

$4.$ All words in EVEN$-$EVEN$*.$