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Fixed a typo (#44)
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Pi-Cla authored Apr 6, 2021
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Expand Up @@ -190,7 +190,7 @@ \chapter{Functional completeness}
$$(A \eand B \eand \enot C) \eor (A \eand \enot B \eand C) \eor (\enot A \eand B \eand \enot C)$$
It follows that the connectives of TFL are jointly functionally complete. We now prove each of the subsidiary results.

\emph{Subsidiary Result \ref{expressive:eor}: functional completeness of `$\enot$' and `$\eor$'.} Observe that the scheme that we generate, using the truth table method of proving the DNF Theorem, will only contain the connectives `$\enot$', `$\eand$' and `$\eor$'. So it suffices to show that there is an equivalent scheme which contains only `$\enot$' and `$\eor$'. To show do this, we simply consider that
\emph{Subsidiary Result \ref{expressive:eor}: functional completeness of `$\enot$' and `$\eor$'.} Observe that the scheme that we generate, using the truth table method of proving the DNF Theorem, will only contain the connectives `$\enot$', `$\eand$' and `$\eor$'. So it suffices to show that there is an equivalent scheme which contains only `$\enot$' and `$\eor$'. To demonstrate this, we simply consider that
\begin{align*}
(\metav{A} \eand \metav{B}) & \text{\quad and \quad} \enot(\enot \metav{A} \eor\enot \metav{B})
\end{align*}
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