Given a set with a subset , the complement (denoted or ) of with respect to is defined as

(1)

Using set difference notation, the complement is defined by

(2)

If , then

(3)

where is the empty set. The complement is implemented in the Wolfram Language as Complement[l, l1, ...].

Given a single set, the second probability axiom gives

(4)

Using the fact that ,

(5)

(6)

This demonstrates that

(7)

Given two sets,

			(8)
			(9)