File:CartDistr.pdf
From formulasearchengine
Jump to navigation
Jump to search
CartDistr.pdf (708 × 531 pixels, file size: 13 KB, MIME type: application/pdf)
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
Summary
DescriptionCartDistr.pdf |
English: Demonstrates the distributivity of the Cartesian product over set intersection, viz. A×(B∩C)=(A×B)∩(A×C), using example sets A = { y∈ℝ: 1≤y≤4 }, B = { x∈ℝ: 2≤x≤5 }, and C = { x∈ℝ: 4≤x≤7 }. Moreover, the distributivity of the Cartesian product over set union and set difference, viz. A×(B∪C)=(A×B)∪(A×C) and A×(B\C)=(A×B)\(A×C), respectively, can be seen from the same example. |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions | File:CartDistr.pdf — File:CartDistr svg.svg |
LaTeX source code |
---|
\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=120mm,paperheight=90mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{120mm}
\setlength{\textheight}{90mm}
\setlength{\evensidemargin}{-2.7cm}
\setlength{\oddsidemargin}{-2.5cm}
\setlength{\parindent}{0cm}
\setlength{\unitlength}{1mm}
\sloppy
\definecolor{cABf} {rgb}{0.70,0.00,0.00} % rectangle AxB foreground
\definecolor{cACf} {rgb}{0.00,0.70,0.00} % rectangle AxC foreground
\definecolor{cABb} {rgb}{0.99,0.80,0.80} % rectangle AxB background
\definecolor{cACb} {rgb}{0.80,0.99,0.80} % rectangle AxC background
\definecolor{cINb} {rgb}{0.99,0.99,0.80} % intersection background
\definecolor{cAf} {rgb}{0.00,0.00,0.70} % interval A
\definecolor{cAxe} {rgb}{0.80,0.80,0.99} % coordinate axes
\definecolor{cEmb} {rgb}{0.90,0.90,0.90} % embedding dots
\begin{document}
\begin{picture}(115,85)
% embedding from intervals to rectangles
\textcolor{cEmb}{\multiput(45,10)(0,1){10}{\makebox(0,0){$\cdot$}}}% B
\textcolor{cEmb}{\multiput(45,26)(0,1){9}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(75,11)(0,1){9}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(75,26)(0,1){9}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(65,12)(0,1){8}{\makebox(0,0){$\cdot$}}}% C
\textcolor{cEmb}{\multiput(65,26)(0,1){9}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(95,12)(0,1){8}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(95,26)(0,1){19}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(12,35)(1,0){8}{\makebox(0,0){$\cdot$}}}% A
\textcolor{cEmb}{\multiput(26,35)(1,0){19}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(12,65)(1,0){8}{\makebox(0,0){$\cdot$}}}%
\textcolor{cEmb}{\multiput(26,65)(1,0){19}{\makebox(0,0){$\cdot$}}}%
% y axis
\textcolor{cAxe}{\put(25.000,20.000){\vector(0,1){60.000}}}%
\textcolor{cAxe}{\multiput(25.000,35.000)(0.000,10.000){5}{\line(-1,0){1.000}}}%
\textcolor{cAxe}{\put(27,80){\makebox(0,0)[l]{$y$}}}%
\textcolor{cAxe}{\put(20,35){\makebox(0,0)[l]{$1$}}}%
\textcolor{cAxe}{\put(20,45){\makebox(0,0)[l]{$2$}}}%
\textcolor{cAxe}{\put(20,55){\makebox(0,0)[l]{$3$}}}%
\textcolor{cAxe}{\put(20,65){\makebox(0,0)[l]{$4$}}}%
\textcolor{cAxe}{\put(20,75){\makebox(0,0)[l]{$5$}}}%
% x axis
\textcolor{cAxe}{\put(20.000,25.000){\vector(1,0){90.000}}}%
\textcolor{cAxe}{\multiput(35.000,25.000)(10.000,0.000){8}{\line(0,-1){1.000}}}%
\textcolor{cAxe}{\put(110,27){\makebox(0,0)[b]{$x$}}}%
\textcolor{cAxe}{\put(35,20){\makebox(0,0)[b]{$1$}}}%
\textcolor{cAxe}{\put(45,20){\makebox(0,0)[b]{$2$}}}%
\textcolor{cAxe}{\put(55,20){\makebox(0,0)[b]{$3$}}}%
\textcolor{cAxe}{\put(65,20){\makebox(0,0)[b]{$4$}}}%
\textcolor{cAxe}{\put(75,20){\makebox(0,0)[b]{$5$}}}%
\textcolor{cAxe}{\put(85,20){\makebox(0,0)[b]{$6$}}}%
\textcolor{cAxe}{\put(95,20){\makebox(0,0)[b]{$7$}}}%
\textcolor{cAxe}{\put(105,20){\makebox(0,0)[b]{$8$}}}%
% x-interval end markers
\textcolor{cABf}{\put(45,7){\line(0,1){2}}}% B
\textcolor{cABf}{\put(75,7){\line(0,1){2}}}%
\textcolor{cACf}{\put(65,9){\line(0,1){2}}}% C
\textcolor{cACf}{\put(95,9){\line(0,1){2}}}%
% y-interval end markers
\textcolor{cAf}{\put(9,35){\line(1,0){2}}}% A
\textcolor{cAf}{\put(9,65){\line(1,0){2}}}%
\thicklines
% x-interval lines and captions
\textcolor{cABf}{\put(45,8){\line(1,0){30}}}% B
\textcolor{cABf}{\put(46,10){\makebox(0,0)[bl]{$B$}}}%
\textcolor{cACf}{\put(65,10){\line(1,0){30}}}% C
\textcolor{cACf}{\put(94,8){\makebox(0,0)[tr]{$C$}}}%
% y-interval lines and captions
\textcolor{cAf}{\put(12,36){\makebox(0,0)[bl]{$A$}}}%
\textcolor{cAf}{\put(10,35){\line(0,1){30}}}% A
% rectangle backgrounds
\textcolor{cABb}{\put(45,35){\makebox(0,0)[bl]{\rule{30mm}{30mm}}}}% A x B
\textcolor{cACb}{\put(65,35.2){\makebox(0,0)[bl]{\rule{30mm}{30mm}}}}% A x C
\textcolor{cINb}{\put(65,35){\makebox(0,0)[bl]{\rule{10mm}{30mm}}}}% intersection
% rectangle borders and captions
\thinlines
\textcolor{cABf}{\put(45,35){\framebox(30,30){}}}% A x B
\textcolor{cABf}{\put(46,36){\makebox(0,0)[bl]{$A \times B$}}}%
\textcolor{cACf}{\put(65,35.2){\framebox(30,30){}}}% A x C
\textcolor{cACf}{\put(94,36){\makebox(0,0)[br]{$A \times C$}}}%
\end{picture}
\end{document}
|
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.
Items portrayed in this file
depicts
21 September 2014
application/pdf
7ebb853e39b18c37cd0678e916a170d98b4140e1
13,446 byte
531 pixel
708 pixel
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 17:06, 21 September 2014 | 708 × 531 (13 KB) | wikimediacommons>Jochen Burghardt | {{Information |Description=Distributivity of Cartesian product and intersection (and union). |Source={{own}} |Date=2014-09-21 |Author=Jochen Burghardt |Permission= |other_versions= }} |
File usage
There are no pages that use this file.
Retrieved from "https://en.formulasearchengine.com/wiki/File:CartDistr.pdf"