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'de Morgan's laws'
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| Title of object: |
de Morgan's laws |
| Canonical Name: |
DeMorgansLaws |
| Type: |
Definition |
| Created on: |
2002-02-20 14:12:07-05 |
| Modified on: |
2002-07-10 23:16:21.036713-04 |
Revision comment (for changes between this and next version):
| Changes for correction # (''). |
Preamble:
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% it should be fine as is for beginners.
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
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%\usepackage{xypic}
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Content:
\emph{de Morgan's laws} hold that, for two sets $A$ and $B$, $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$, where $\cup$ denotes the union, $\cap$ denotes the intersection, and $'$ denotes the set complement.
If $A,B \subset I$, then
$$A \cup B \equiv \{x:x \in A \lor x \in B\}$$
$$A \cap B \equiv \{x:x \in A \land x \in B\},$$
related to the familiar relations of Boolean Algebra: $(A \land B)' = A' \lor B'$ and $(A \lor B)' = A' \land B'$. |
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