A U
(B U
C) = (A U
B) U
C
A union (B union
C) equals (A union
B) union C
This law states that taking the union of a set to the
union of two other sets is the same as taking the union of the original set
and one of the other two sets, and then taking the union of the results with
the last set.
A 
(B C)
= (A
B) C
A intersection (B intersection C)
equals (A intersection B)
intersection C
This law states that taking the intersection of a set to the intersection
of two other sets is the same as taking the intersection of the original set
and one of the other two sets, and then taking the intersection of the results
with the last set.