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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:
AuB « C =
(A » B) C
AC » BC = AC u BC
(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» {1 2 3 4 5 6} 6*1/6
A « B« C {} 0*1/6

Last Update: 2005-Jšn-25