$(1)$ The crazy giraffe behind that tree will chase the hungry lion

I've provided three Phrase Structure Grammars below in $($i$)-($iii$).$ These three grammars will all successfully generate

the sentence in $(1).$ However, the resulting structures that they generate have significant differences.

$($i$)$ PSG $1$

S $$ D Adj N P D N Aux V Det Adj N

$($ii$)$ PSG $2$

$S,$ NP Aux VP

$NP$ D Adj N P Det N

$VP{V}_{T}D$ Adj $N$

$($iii$)$ PSG $3$

$S,,NP$ AuxP

AuxP$$ Aux VP

$VP,,V_{T}NP$

$NP,,D($Adj$)$ N $($PP$)$

$PP,,P$ NP

Task A

Draw the syntactic tree for the sentence in $(1),$ first using PSG $1,$ then PSG $2,$ and finally PSG $3.($You should have

drawn three trees altogether.$)$

Task $B{?}_{(}())$

Determine which PSG does a better job generating $(1)$ and explain why it does a better job? $($Hint: think about which

one is better in terms of constituency.$)$