For each of the following context free grammars $($i$)-($iv$)$:

a$)$ Use the set notations, $L(G)=(V,,P,S)$ to define the language generated by the grammar.

b$)$ Apart of lambda $($if any$),$ what is the shortest string that can be produced from the grammar?

c$)$ Write three other strings that can be generated from the languages.

i$)$

$S$aaSB$||$

$BbB|b|$

ii$)$

$S$aSbb$|A|$

$ACA|c|$

iii$)$

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

$A$cdAba$||$

iv$)$

$S$aSb$|A|$

$A$cAd$|cBd|$

$B$aBb$|ab|$