Mathematik-Online lexicon: Implications of Laws for Operations on Sets

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematik-Online lexicon:
	Implications of Laws for Operations on Sets

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

De Morgan's Laws imply, for instance,

$\displaystyle C\setminus (A\cap C)$	$\displaystyle =$	$\displaystyle (C\setminus A)\cup (C\setminus C)\;=\;(C\setminus A)\cup \emptyset\;=\;C\setminus A\,,$
$\displaystyle C\setminus (A\cup C)$	$\displaystyle =$	$\displaystyle (C\setminus A)\cap (C\setminus C)\;=\;(C\setminus A)\cap \emptyset\;=\;\emptyset \,.$

It follows from the distributive laws, that

$\displaystyle (A\cup B)\cap B$

$\displaystyle =$

$\displaystyle (A\cap B)\cup (B\cap B)\;=\;(A\cap B)\cup B\,.$

Here it is $(A\cap B)\cup B=B$ , since $(A\cap B)\subseteq B$ .

(Authors: Wipper/Abele)

automatisch erstellt am 6. 6. 2006