Here's a guide to working with set notations:

P = Everything in P
Q = Everything in Q

P' [pronounced P prime] = Everything not in P
Note: P' is also known as the 'complement'

U = union of sets [basically, addition]
P U Q = Everything in P and everything in Q
P' U Q = Everything not in P and everything in Q

n = intersect [both must have]
P n Q = Everything that is in both P AND Q
P n Q' = Everything that is in both P AND not in Q

When you have complex sets like (P' U Q)' for instance, identify what the inside parts are first in terms of shaded area, then just apply the complement next (i.e. shaded becomes unshaded, unshaded becomes shaded).

Breaking your sets down into pieces can help you not get overwhelmed by them.