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Add content to 1_kartesisches_produkt_relationen.md

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Niklas Birk
2022-09-23 17:11:38 +02:00
parent 980c9ae69a
commit 2cb5c1cf88
8 changed files with 506 additions and 98 deletions
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78
assets/mathematik/mengenlehre/inverse_rel.tex Normal file
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\documentclass[convert={size=512}]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{color}
\definecolor{draculaPurple}{RGB}{189,147,249}
\definecolor{draculaCyan}{RGB}{139,233,253}
\definecolor{draculaForeground}{RGB}{248,248,248}
\definecolor{draculaRed}{RGB}{255, 85, 85}
\begin{document}
\begin{tikzpicture}[text=draculaForeground, draw=draculaCyan]
% Set names
\node at (0,-0.4) [thick] {A};
\node at (3,-0.4) [thick] {B};
% Set elements
\begin{scope}[every node/.style={circle,thick,draw}]
\node (1) at (0,-1) {1};
\node (2) at (0,-2) {2};
\node (3) at (0,-3) {3};
\node (4) at (0,-4) {4};
\node (5) at (0,-5) {5};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (A) at (3,-1.5) {a};
\node (B) at (3,-2.5) {b};
\node (C) at (3,-3.5) {c};
\node (D) at (3,-4.5) {d};
\end{scope}
% Arrows
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (1) edge (A);
\path [->] (1) edge (D);
\path [->] (2) edge (B);
\path [->] (3) edge (B);
\path [->] (4) edge (D);
\end{scope}
% Compose
\begin{scope}
\node at (4.5,-2.5) {\huge $\overset{R^{-1}}{\Longrightarrow}$};
\end{scope}
% Set names
\node at (6,-0.4) [thick] {B};
\node at (9,-0.4) [thick] {A};
% Set elements
\begin{scope}[every node/.style={circle,thick,draw}]
\node (AA) at (6,-1.5) {a};
\node (BB) at (6,-2.5) {b};
\node (CC) at (6,-3.5) {c};
\node (DD) at (6,-4.5) {d};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (11) at (9,-1) {1};
\node (22) at (9,-2) {2};
\node (33) at (9,-3) {3};
\node (44) at (9,-4) {4};
\node (55) at (9,-5) {5};
\end{scope}
% Arrows
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (AA) edge (11);
\path [->] (BB) edge (22);
\path [->] (BB) edge (33);
\path [->] (DD) edge (11);
\path [->] (DD) edge (44);
\end{scope}
\end{tikzpicture}
\end{document}

56
assets/mathematik/mengenlehre/verkettung_1.tex Normal file
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@ -0,0 +1,56 @@
\documentclass[convert={size=384}]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{color}
\definecolor{draculaPurple}{RGB}{189,147,249}
\definecolor{draculaCyan}{RGB}{139,233,253}
\definecolor{draculaForeground}{RGB}{248,248,248}
\begin{document}
\begin{tikzpicture}[text=draculaForeground, draw=draculaCyan]
% Set names
\node at (0,-0.4) [thick] {A};
\node at (3,-0.4) [thick] {B};
\node at (6,-0.4) [thick] {C};
% Set elements
\begin{scope}[every node/.style={circle,thick,draw}]
\node (1) at (0,-1) {1};
\node (2) at (0,-2) {2};
\node (3) at (0,-3) {3};
\node (4) at (0,-4) {4};
\node (5) at (0,-5) {5};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (A) at (3,-1.5) {a};
\node (B) at (3,-2.5) {b};
\node (C) at (3,-3.5) {c};
\node (D) at (3,-4.5) {d};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (x) at (6,-2) {$\alpha$};
\node (y) at (6,-3) {$\beta$};
\node (z) at (6,-4) {$\gamma$};
\end{scope}
% Arrows
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (1) edge (A);
\path [->] (1) edge (D);
\path [->] (2) edge (B);
\path [->] (3) edge (B);
\path [->] (4) edge (D);
\end{scope}
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (A) edge (x);
\path [->] (A) edge (y);
\path [->] (A) edge (z);
\path [->] (B) edge (y);
\path [->] (C) edge (x);
\end{scope}
\end{tikzpicture}
\end{document}

89
assets/mathematik/mengenlehre/verkettung_2.tex Normal file
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@ -0,0 +1,89 @@
\documentclass[convert={size=512}]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{color}
\definecolor{draculaPurple}{RGB}{189,147,249}
\definecolor{draculaCyan}{RGB}{139,233,253}
\definecolor{draculaForeground}{RGB}{248,248,248}
\definecolor{draculaRed}{RGB}{255, 85, 85}
\begin{document}
\begin{tikzpicture}[text=draculaForeground, draw=draculaCyan]
% Set names
\node at (0,-0.4) [thick] {A};
\node at (3,-0.4) [thick] {B};
\node at (6,-0.4) [thick] {C};
% Set elements
\begin{scope}[every node/.style={circle,thick,draw}]
\node (1) at (0,-1) {1};
\node (2) at (0,-2) {2};
\node (3) at (0,-3) {3};
\node (4) at (0,-4) {4};
\node (5) at (0,-5) {5};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (A) at (3,-1.5) {a};
\node (B) at (3,-2.5) {b};
\node (C) at (3,-3.5) {c};
\node (D) at (3,-4.5) {d};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (x) at (6,-2) {$\alpha$};
\node (y) at (6,-3) {$\beta$};
\node (z) at (6,-4) {$\gamma$};
\end{scope}
% Arrows
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (1) edge[draw=draculaRed] (A);
\path [->] (1) edge (D);
\path [->] (2) edge[draw=draculaRed] (B);
\path [->] (3) edge[draw=draculaRed] (B);
\path [->] (4) edge (D);
\end{scope}
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (A) edge[draw=draculaRed] (x);
\path [->] (A) edge[draw=draculaRed] (y);
\path [->] (A) edge[draw=draculaRed] (z);
\path [->] (B) edge[draw=draculaRed] (y);
\path [->] (C) edge (x);
\end{scope}
% Compose
\begin{scope}
\node at (7.5,-3) {\Huge $\overset{R \circ K}{\Longrightarrow}$};
\end{scope}
% Set names
\node at (9,-0.4) [thick] {A};
\node at (12,-0.4) [thick] {C};
% Set elements
\begin{scope}[every node/.style={circle,thick,draw}]
\node (11) at (9,-1) {1};
\node (22) at (9,-2) {2};
\node (33) at (9,-3) {3};
\node (44) at (9,-4) {4};
\node (55) at (9,-5) {5};
\end{scope}
\begin{scope}[every node/.style={circle,thick,draw}]
\node (xx) at (12,-2) {$\alpha$};
\node (yy) at (12,-3) {$\beta$};
\node (zz) at (12,-4) {$\gamma$};
\end{scope}
% Arrows
\begin{scope}[every edge/.style={draw=draculaPurple,very thick}]
\path [->] (11) edge (xx);
\path [->] (11) edge (yy);
\path [->] (11) edge (zz);
\path [->] (22) edge (yy);
\path [->] (33) edge (yy);
\end{scope}
\end{tikzpicture}
\end{document}