Problem $1$

Let $G=(T,V,S,P)$ be a context$-$free grammar with

$T=\{a,b,c\}$

$V=\{S,A,B\}$

Productions P :

$SAB|ScS|$

B $$ bB $|$b

$AaA|||$

a$.$ Find a leftmost derivation of $w=$abcaabbcb

b$.$ Hand draw a parse tree for bbcabcabb. What is the longest path from S to a leaf in your parse tree? Paste your parse tree into Homework $5.$

c$.$ Hand draw a parse for $w=$ bcccab. What is the longest path from $S$ to a leaf in your parse tree? Paste your parse tree into Homework $5.$

d$.$ Why is it impossible to derive $w=$ baa using G$?$ Justify your answer.