For each of the following context$-$free grammars, use set notation to define the language generated by the grammar.

a$)$

$S$aaSB$||$

$BbB|b|$

b$)$

$S$aSbb$|A|$

$AcA|c|$

c$)$

$S\frac{}{a}bSdc|A|$

$A$cdAba$||$

d$)$

$S$aSb$|A|$

$A$cAd$|cBd|$

$B$aBb$|ab|$

e$),S$aSB$|aB|$