PrepZii

table

Algebra of Sets

The source groups the standard algebraic laws of sets before counting formulas.

Law	Formulae
Commutative	$(A\cup B)=B\cup A;\quad A\cap B=B\cap A$
Associative	$(A\cup B)\cup C=A\cup(B\cup C);\quad (A\cap B)\cap C=A\cap(B\cap C)$
Distributive	$A\cup(B\cap C)=(A\cup B)\cap(A\cup C);\quad A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$
De Morgan	$(A\cup B)'=A'\cap B';\quad (A\cap B)'=A'\cup B'$
Identity	$A\cap U=A;\quad A\cup\phi=A$
Complement	$A\cup A'=U,\quad A\cap A'=\phi,\quad (A')'=A$
Idempotent	$A\cap A=A,\quad A\cup A=A$