diff --git a/Tutorials/T11-FinalReview/Exam Review.pptx b/Tutorials/T11-FinalReview/Exam Review.pptx index 53f3b06af937754468004690e7b8a69e1bf26d02..3908c54d58c62b7c105faa50336c00372a1fd605 100644 Binary files a/Tutorials/T11-FinalReview/Exam Review.pptx and b/Tutorials/T11-FinalReview/Exam Review.pptx differ diff --git a/Tutorials/T11-FinalReview/document.pdf b/Tutorials/T11-FinalReview/document.pdf new file mode 100644 index 0000000000000000000000000000000000000000..405a9c9efa1f14fcd3bff2da221cce20643be60d Binary files /dev/null and b/Tutorials/T11-FinalReview/document.pdf differ diff --git a/Tutorials/T11-FinalReview/document.tex b/Tutorials/T11-FinalReview/document.tex new file mode 100644 index 0000000000000000000000000000000000000000..4579b0d2c0e00338da747e95877dd8cffcb7c52c --- /dev/null +++ b/Tutorials/T11-FinalReview/document.tex @@ -0,0 +1,19 @@ +\documentclass[12pt,fleqn]{article} +\usepackage{graphicx} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{listings} +\usepackage{url} + +\newcommand\tab[1][0.8cm]{\hspace*{#1}} + +\begin{document} + \begin{eqnarray*} + \lefteqn{\forall (i, j: \mathbb{N} | 0 \leq i < 2 \wedge 0 \leq j < 2 :}\\ + && \exists(k, l: \mathbb{N} | 0 \leq k < 2 \wedge 0 \leq l < 2 \wedge (k \neq i \wedge l \neq j) : \\ + && \tab \exists(m, n: \mathbb{N} | 0 \leq m < 2 \wedge 0 \leq n < 2 + \wedge (m \neq k \wedge n \neq j) \\ + && \tab \wedge i - k = -( i - m) \wedge j - l = -( j - n) ) : \\ + && \tab \tab board[i][j] = board[k][l] = board[m][n] ) + \end{eqnarray*} +\end{document} \ No newline at end of file