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box-o-sand/math-replay/algebra/new-definitions-1.haml

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%html
%head
%title New Definitions 1
%script{:type => "text/x-mathjax-config"}
MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
%script{:type => "text/javascript", :src => "http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"}
%link{:rel => 'stylesheet', :type => 'text/css', :href => './style.css'}
%body
%h2 $x `not` $y = 8x - 3y$:
:eqnarray
x `not` y & = & 8x - 3y \\
6 `not` -2 & = & 8(6) - 3(-2) \\
6 `not` -2 & = & 48 + 6 \\
6 `not` -2 & = & 54 \\
%h2 $x `star` y = 8y + 2$:
:eqnarray
x `star` y & = & 8y + 2 \\
-2 `star` 5 & = & 8(5) + 2 \\
-2 `star` 5 & = & 40 + 2 \\
-2 `star` 5 & = & 42 \\
%h2 $x `diamond` y = xy + 3x - y$:
:eqnarray
x `diamond` y & = & xy + 3x - y \\
3 `diamond` -2 & = & (3)(-2) + 3(3) - (-2) \\
3 `diamond` -2 & = & -6 + 9 + 2 \\
3 `diamond` -2 & = & -6 + 11 \\
3 `diamond` -2 & = & 5 \\
%h2 $x `not` y = x + 3y$:
:eqnarray
x `not` y & = & x + 3y \\
-4 `not` 6 & = & -4 + 3(6) \\
-4 `not` 6 & = & -4 + 18 \\
-4 `not` 6 & = & 14 \\
%h2 $x `donut` y = 3x - 3y$:
:eqnarray
x `donut` y & = & 3x - 3y \\
0 `donut` 0 & = & 3(0) - 3(0) \\
0 `donut` 0 & = & 0 - 0 \\
0 `donut` 0 & = & 0 \\