File:CartInts.pdf
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Summary
DescriptionCartInts.pdf |
English: Demonstrates the compatibility of the Cartesian product and set intersection, viz. (A∩B)×(C∩D)=(A×C)∩(B×D), using example sets A = { x∈ℝ: 2≤x≤5 }, B = { x∈ℝ: 3≤x≤7 }, C = { y∈ℝ: 1≤y≤3 }, and D = { y∈ℝ: 2≤y≤4 }. |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions | File:CartInts.pdf — File:CartInts svg.svg |
LaTeX source code |
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\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}
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\sloppy
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\definecolor{cBDf} {rgb}{0.00,0.70,0.00} % rectangle BxD foreground
\definecolor{cACb} {rgb}{0.99,0.80,0.80} % rectangle AxC background
\definecolor{cBDb} {rgb}{0.80,0.99,0.80} % rectangle BxD background
\definecolor{cINf} {rgb}{0.70,0.70,0.00} % intersection foreground
\definecolor{cINb} {rgb}{0.99,0.99,0.80} % intersection background
\definecolor{cAxe} {rgb}{0.80,0.80,0.99} % coordinate axes
\definecolor{cEmb} {rgb}{0.90,0.90,0.90} % embedding dots
\begin{document}
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% embedding from intervals to rectangles
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\textcolor{cEmb}{\multiput(55,12)(0,1){8}{\makebox(0,0){$\cdot$}}}% B
\textcolor{cEmb}{\multiput(55,26)(0,1){9}{\makebox(0,0){$\cdot$}}}%
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% y axis
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% x axis
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% x-interval end markers
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\textcolor{cBDf}{\put(95,9){\line(0,1){2}}}%
\textcolor{cINf}{\put(55,6.5){\line(0,1){2}}}% A n B
\textcolor{cINf}{\put(75,6.5){\line(0,1){2}}}%
% y-interval end markers
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\textcolor{cBDf}{\put(9,65){\line(1,0){2}}}%
\textcolor{cINf}{\put(6.5,45){\line(1,0){2}}}% C n D
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\thicklines
% x-interval lines and captions
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\textcolor{cBDf}{\put(94,8){\makebox(0,0)[tr]{$B$}}}%
\textcolor{cINf}{\put(55,7.5){\line(1,0){20}}}% A n B
% y-interval lines and captions
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% rectangle backgrounds
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\textcolor{cBDb}{\put(55,45){\makebox(0,0)[bl]{\rule{40mm}{20mm}}}}% B x D
\textcolor{cINb}{\put(55,45){\makebox(0,0)[bl]{\rule{20mm}{10mm}}}}% intersection
% rectangle borders and captions
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\textcolor{cACf}{\put(45,35){\framebox(30,20){}}}% A x C
\textcolor{cACf}{\put(46,36){\makebox(0,0)[bl]{$A \times C$}}}%
\textcolor{cBDf}{\put(55,45){\framebox(40,20){}}}% B x D
\textcolor{cBDf}{\put(94,64){\makebox(0,0)[tr]{$B \times D$}}}%
\end{picture}
\end{document}
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Licensing
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Items portrayed in this file
depicts
21 September 2014
application/pdf
6107030ae5eae294d904350d392c9a8e109b43a6
13,768 byte
531 pixel
708 pixel
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:08, 21 September 2014 | 708 × 531 (13 KB) | Jochen Burghardt | {{Information |Description=Intersection of Cartesian products |Source={{own}} |Date=2014-09-21 |Author=Jochen Burghardt |Permission= |other_versions= }} |
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Software used | TeX |
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Conversion program | pdfTeX-1.40.3 |
Encrypted | no |
Page size | 340.157 x 255.118 pts |
Version of PDF format | 1.4 |
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