please explain your answer and your process$($a$)(5$pts$)$ Construct a context free grammar over $\{a,b,c\}$ whose language is $\{a^n{b}^{2n}{c}^m|n,m>0\}.$

$($b$)(5$pts$)$ Construct a context free grammar over $\{a,b\}$ whose language is $\{a^m{b}^n|0nm3n\}.$

$(10$pts$)$ Write a CFG to generate identifiers $($IDs$)$ in the Java Programming Language. An ID in Java

is a string of characters consisting of letters $($upper$-$level or lower$-$level$),$ digits, underscore $\_,$ or

dollar sign $$.$ It cannot start with a digit.

$(10$pts$)$ Using your grammar created in problem $1,$ give a leftmost derivation, AND draw the tree for

the derivation for the identifier $$$1uP.$