Calculating with Sets

When combining two or more sets by union or intersection, the following rules have to be applied:
 
 

Commutative Law	A B = B A
Associative Law	(A B) C = A (B C)
Distributive Law	(A B) C =  (A C) (B C)
De Morgan's Laws	~(A B) = ~A   ~B ~(A  B) = ~A   ~B

A visualization of the distributive law:

			=
(A B)		C
			=
(A C)		(B C)		(A C) (B C)

Example:

When we define an additional event C {number larger than 1} and calculate the union and intersection of all three events A, B and C, we find that the probability of the union equals 1 and the probability of the intersection is zero. Event Sample points Probability A { 2 4 6} 3*1/6 B {1 2 3} 3*1/6 C {2 3 4 5 6} 5*1/6 A B C  {1 2 3 4 5 6} 6*1/6 A B C {} 0*1/6