Based on the following grammar:

NounPhrase $>$ VerbPhrase$>$

$$

$$ Verb$>$

$$ Article$>$ the

$$ Noun $>$ man $|$ ball

$$ Verb$>$ hit $|$ took

$a.$ Show the left derivation $of$ "the man took the ball"

$b.$ Show the right derivation $of$ "the man hit the man"

$c.$ Show parse trees $(right$ & left$)$ for "the man hit the ball". $Is$ this $an$

unambiguou$\frac{s}{a}$mbiguous grammar? Feel free $to$ draw them $on$ a piece $of$ paper

and then input a picture.

$d.$ Are the following valid sentences $in$ this grammar

$i.$ the man hit the man

$ii.$ the man hit a ball

iii. the ball hit the man

$iv.$ the ball the man hit