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thatbelongtoA
and
donotbelongtoB.ThedifferenceofAandBmaybethus
described
like
this:
A
\
B
=
{
x
:
x
∈
A
∧
x
∉
B
}
or
like
this:
x
∈\
A
B
⇔
x
∈
A
∧
¬
x
∈
B
.ThedifferenceisillustratedinFig.2.4.
A
A\B
B
U
Fig02040Differenceoftwosets
Similarlyasinthecaseofthelogicformulae,alsoherewecanlistsome
importantformulaewhicharealwaystrue,calledthe
setalgebralaws
.Theyare
listedinTable2.1.
Table2010Importantsetalgebralaws
Law
(A′)′=A
A∩A′=∅
A∪A′=U
A∪B=B∪A
A∩B=B∩A
A∪(B∪C)=(A∪B)∪C
A∩(B∩C)=(A∩B)∩C
A∪(B∩C)=(A∪B)∩(A∪C)
A∩(B∪C)=(A∩B)∪(A∩C)
A∩U=A
A∪U=U
A∩∅=∅
A∪∅=A
(A∪B)′=A′∩B′
(A∩B)′=A′∪B′
Name
Involutionlaw
Complementlaws
Commutativelaws
Associativelaws
Distributivelaws
Absorptionlaws
DeMorgan’slaws
25
