What can you say about A and B if we know that:

a) A &cup B = A
B has to be a nullset because of the identity law.

b) A &cap B = A
A has to be a complete subset of B. All the elements of a are also elements of B

c) A - B = A
A does not intersect with B at all.

d) A &cap B = B &cap A
We can't know anything about the sets because this is the Commutative law

e) A - B = B - A
A and B have to be equal or of have no elements in common.