MyWikiBiz, Author Your Legacy — Sunday November 24, 2024
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90 bytes added
, 11:14, 24 August 2009
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| <math>\begin{matrix} | | <math>\begin{matrix} |
| \texttt{()} | | \texttt{()} |
| + | & = & \nu_0 |
| & = & 0 | | & = & 0 |
| & = & \operatorname{false} | | & = & \operatorname{false} |
| \\[6pt] | | \\[6pt] |
| \texttt{(x)} | | \texttt{(x)} |
| + | & = & \nu_1 (x) |
| & = & \tilde{x} | | & = & \tilde{x} |
| & = & x^\prime | | & = & x^\prime |
| \\[6pt] | | \\[6pt] |
| \texttt{(x, y)} | | \texttt{(x, y)} |
| + | & = & \nu (x, y) |
| & = & \tilde{x}y \lor x\tilde{y} | | & = & \tilde{x}y \lor x\tilde{y} |
| & = & x^\prime y \lor x y^\prime | | & = & x^\prime y \lor x y^\prime |
| \\[6pt] | | \\[6pt] |
| \texttt{(x, y, z)} | | \texttt{(x, y, z)} |
| + | & = & \nu (x, y, z) |
| & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} | | & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} |
| & = & x^\prime y z \lor x y^\prime z \lor x y z^\prime | | & = & x^\prime y z \lor x y^\prime z \lor x y z^\prime |
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| |} | | |} |
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− | Expressing the general case of <math>\nu_k\!</math> in terms of familiar operations is facilitated by making a preliminary definition.
| + | To express the general case of <math>\nu_k\!</math> in terms of familiar operations, it helps to make a preliminary definition. |
| | | |
− | '''Definition.''' Let the function <math>\lnot_j : \mathbb{B}^k \to \mathbb{B},</math> for each integer <math>j \in [1, k],</math> be defined by the following equation: | + | '''Definition.''' Let the function <math>\lnot_j : \mathbb{B}^k \to \mathbb{B},</math> where <math>j\!</math> is an integer in the interval <math>[1, k],\!</math> be defined by the following equation: |
| | | |
| {| align="center" cellpadding="8" width="90%" | | {| align="center" cellpadding="8" width="90%" |