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MyWikiBiz, Author Your Legacy — Sunday November 24, 2024
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expand a bit
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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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|}
 
|}
   −
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%"
12,080

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