diff --git a/Tutorials/T11-FinalReview/Exam Review.pptx b/Tutorials/T11-FinalReview/Exam Review.pptx index a3f478afb973579b5b8bd162e4722d7298eb328d..7ce4676b6d731510098115e0a1063e10c45431de 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 index 405a9c9efa1f14fcd3bff2da221cce20643be60d..805fd3984d5b5a9214fd8d43f1646d9556ef6aaa 100644 Binary files a/Tutorials/T11-FinalReview/document.pdf and b/Tutorials/T11-FinalReview/document.pdf differ diff --git a/Tutorials/T11-FinalReview/document.tex b/Tutorials/T11-FinalReview/document.tex index 4579b0d2c0e00338da747e95877dd8cffcb7c52c..10b28c531f80999ca08e045fc612806e827793e9 100644 --- a/Tutorials/T11-FinalReview/document.tex +++ b/Tutorials/T11-FinalReview/document.tex @@ -8,12 +8,12 @@ \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*} + \begin{eqnarray*} + \lefteqn{\forall (i, j: \mathbb{N} | 0 \leq i < SIZE \wedge 0 \leq j < SIZE :}\\ + && \exists(k, l: \mathbb{N} | 0 \leq k < SIZE \wedge 0 \leq l < SIZE \wedge (k \neq i \wedge l \neq j) : \\ + && \tab \exists(m, n: \mathbb{N} | 0 \leq m < SIZE \wedge 0 \leq n < SIZE + \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