Given the following syntactic rules, generate syntax trees for each sentence. $($There are two trees for both sentences$).$

S $->$ DP VP VP $->$ V

DP $->$ D NP VP $->$ V AP VP $->$ VP CP

NP $->$ AP NP VP $->$ VP PP PP $->$ P DP

NP $->$ N AP $->$ A CP $->$ C S

NP $->$ NP PP

VP $->$ V DP

a$)$ The dog chased a cat under the table.

b$)$ A slow class on every topic ended.