Given a set S with a subset E, the complement (denoted E' or E^_) of E with respect to S is defined as E' congruent {F:F element S, F not element E}. Using set difference notation, the complement is defined by E' = S\E. If E = S, then E' congruent S' = ∅, 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 1 = P(S) = P(E union E').

intersection | Poretsky's law | set difference | symmetric difference | universal set