Pr(X|Y) denotes the probability that X occurs given that Y occurs
Pr(X U Y) denotes the probability of the union of events X and Y, that is the probability that one or other or both occur.
If C and D are independednt Pr(C and D)=Pr(C)Pr(D) - this is the definition of independednce.
Also: Pr(C and D)=Pr(C|D)Pr(D).
That should be sufficient to do part (a)
For part (b) you need:
Pr(C U D)=Pr(C)+Pr(D)-Pr(C and D)