diff --git a/Tutorials/T11-FinalReview/Exam Review.pptx b/Tutorials/T11-FinalReview/Exam Review.pptx index a4ff68c82241475374371747e07806f620bdeb11..a801a26f6eb8a07a4030811f30df79e3a85ca302 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 4658cceaa90ffbf3f14461b0fde0b6e5396ec4ee..5fd75b4983c22501d889eef5956563a19b1b6439 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 06e0002b7dcc37659b5d37c43f6f79f761ad9b2f..9150312c46f3e57df937fde0fb4f515124dcd138 100644 --- a/Tutorials/T11-FinalReview/document.tex +++ b/Tutorials/T11-FinalReview/document.tex @@ -9,7 +9,7 @@ \begin{document} \noindent -$\forall (i, j: \mathbb{N} ~|~ 0 \leq i < SIZE \wedge 0 \leq j < SIZE : \newline +$\exists (i, j: \mathbb{N} ~|~ 0 \leq i < SIZE \wedge 0 \leq j < SIZE : \newline ~\qquad \mbox{checkHoriz}(i, j) \lor \mbox{checkVert}(i, j) \lor \mbox{checkDiag}(i, j))$\\ \noindent{\bf local functions}\\ @@ -18,13 +18,13 @@ $\mbox{checkHoriz}(i, j) \equiv (\newline ~\qquad i + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i+1][j] \land board[i][j] = board[i+2][j] \newline )$\\[\baselineskip] -checkHoriz: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ -$\mbox{checkHoriz}(i, j) \equiv (\newline +checkVert: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ +$\mbox{checkVert}(i, j) \equiv (\newline ~\qquad j + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i][j+1] \land board[i][j] = board[i][j+2] \newline )$\\[\baselineskip] checkDiag: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ -$\mbox{checkHoriz}(i, j) \equiv (\newline +$\mbox{checkDiag}(i, j) \equiv (\newline ~\qquad i + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad j + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i+1][j+1] \land board[i][j] = board[i+2][j+2] \newline