Jirka_RA: Solution: Exercise 0.3.7

Books/Jirka_RA/Chapter00/Ex0_3/ex07.gapry.tex

@@ -0,0 +1,132 @@
+\subsubsection*{Exercise 0.3.7. (Gapry)}
+
+\begin{flushleft}
+
+\textbf{Part B} \\
+\begin{tikzpicture}
+    \begin{scope}[shift={(-6, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \fill[even odd rule, gray] \firstcircle \secondcircle;
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+
+        \node[below] at (0, -2.3) {A $\triangle$ B};
+    \end{scope}
+
+    \node at (-3.5,0) {$=$};
+
+    % Figure 2: Venn diagram of A \ B
+    \begin{scope}[shift={(-1, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \begin{scope}
+            \clip \firstcircle ;
+            \fill[gray,even odd rule] \firstcircle \secondcircle;
+        \end{scope}
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+        \node[below] at (0,-2.3) {A $\setminus$ B};
+    \end{scope}
+
+    \node at (1.5,0) {$\cup$};
+
+    % Figure 3: Venn diagram of B \ A
+    \begin{scope}[shift={(4, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \begin{scope}
+            \clip \secondcircle;
+            \fill[gray,even odd rule] \secondcircle \firstcircle;
+        \end{scope}
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+        \node[below] at (0, -2.3) {B $\setminus$ A};
+    \end{scope}
+\end{tikzpicture}
+
+\textbf{Part C} \\
+\begin{tikzpicture}
+    \begin{scope}[shift={(-6, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \fill[even odd rule, draw = black, fill = lightgray] \firstcircle \secondcircle;
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+
+        \node[below] at (0, -2.3) {A $\triangle$ B};
+    \end{scope}
+
+    \node at (-3.5,0) {$=$};
+
+    % Figure 2: Venn diagram of A union B
+    \begin{scope}[shift={(-1, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \begin{scope}
+            \filldraw[draw = black, fill = lightgray] \firstcircle \secondcircle;
+        \end{scope}
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+        \node[below] at (0, -2.3) {A $\cup $ B};
+    \end{scope}
+
+    \node at (1.5,0) {$\setminus$};
+
+    % Figure 3: Venn diagram of A intersection B
+    \begin{scope}[shift={(4, 0)}]
+        \def\firstcircle  {(-0.5, -0.5) circle(1)}
+        \def\secondcircle {( 0.5,  0.5) circle(1)}
+
+        \draw (-2,-2) rectangle (2, 2);  % Draw the universe set S
+        \draw \firstcircle;              % Draw subset A
+        \draw \secondcircle;             % Draw subset B
+
+        \begin{scope}
+            \clip \firstcircle ;
+            \fill[draw = black, fill = lightgray] \secondcircle;
+        \end{scope}
+
+        \node at (-1.5,  1.5) {$S$};  % Label the universe set 
+        \node at (-0.5, -0.5) {$A$};  % Label subset A
+        \node at ( 0.5,  0.5) {$B$};  % Label subset A
+        \node[below] at (0, -2.3) {A $\cap$ B};
+    \end{scope}
+\end{tikzpicture}
+
+\end{flushleft}

Utility/base.tex

@@ -3,4 +3,5 @@
 \usepackage{amsfonts}
 \usepackage{pgffor}   % sudo apt install texlive-latex-extra
 \usepackage{hyperref}
-\usepackage{cancel}
+\usepackage{cancel}
+\usepackage{tikz}