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Anisomorphism
Joined 24 January 2021
→Algebraic Geometry of Computing
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XOR is only "true" or 1 when x or y but not both, are 1. Disjunctive normal form says that we can view the x, y entries as unary operators which return the input with no change, combine these as given on the lines which evaluate to 1, and take the OR of all of them for the total connective form of the truth table. Here is the | XOR is only "true" or 1 when x or y but not both, are 1. Disjunctive normal form says that we can view the x, y entries as unary operators which return the input with no change, combine these as given on the lines which evaluate to 1, and take the OR of all of them for the total connective form of the truth table. Here is the third line: <math> x\and\neg y</math>. | ||
<br> The total is: | |||
<math> | |||
\begin{align*} | |||
&(x\and\neg y)\or (\neg x\and y) \\ | |||
=&(x\or(\neg x\and y))\and(\neg y\or(\neg x\and y)) \\ | |||
=&(x\or\neg x)\and (x\or y)\and(\neg y\or\neg x)\and(\neg y\or y) \\ | |||
=&(x\or y)\and (\neg y\or\neg x) \\ | |||
=&(x\or y)\and\neg (y\and x) | |||
\end{align*} | |||
</math> | |||
<br> | |||
This process can be viewed as a sum of "elementary functions" which are only 1 on one line each, and building a general function/table. | |||
= Read prototype = | = Read prototype = | ||