Have a few problems with my assignment.

Circuit is as follows:

Ive derived a truth table and come up with this :

Can someone verify if the above is correct?

Ive then got these 2 logic expressions :

Y = A'D' + C'D' + B'D'

Z = D+ B

What I want to know is (if the above is correct) Is it possible to implement the above circuit using fewer logic gates?