Changes

If the list of arguments is empty, as expressed in the form <math>\texttt{Mno}(),</math> then it cannot be true that exactly one of the arguments is false, so <math>\texttt{Mno}() = \texttt{False}.</math>

If the list of arguments is empty, as expressed in the form <math>\texttt{Mno}(),</math> then it cannot be true that exactly one of the arguments is false, so <math>\texttt{Mno}() = \texttt{False}.</math>

If <math>\texttt{p}</math> is the only argument, then <math>\texttt{Mno(p)}</math> says that <math>\texttt{p}</math> is false, so <math>\texttt{Mno(p)} = \texttt{Not(p)}.</math>

If <math>p\!</math> is the only argument, then <math>\texttt{Mno}(p)</math> says that <math>p\!</math> is false, so <math>\texttt{Mno}(p)</math> expresses the logical negation of the proposition <math>p\!</math>, which may be expressed by any one of the equivalent forms, <math>\texttt{Mno}(p) = \texttt{Not}(p) = \lnot p = \tilde{p} = p^\prime.</math>

If <math>\texttt{p}</math> and <math>\texttt{q}</math> are the only two arguments, then <math>\texttt{Mno(p, q)}</math> says that exactly one of <math>\texttt{p, q}</math> is false, so <math>\texttt{Mno(p, q)}</math> says the same thing as <math>\texttt{p} \neq \texttt{q}.</math>

If <math>p\!</math> and <math>q\!</math> are the only two arguments, then <math>\texttt{Mno}(p, q)</math> says that exactly one of <math>p, q\!</math> is false, so <math>\texttt{Mno}(p, q)</math> says the same thing as <math>p \neq q.\!</math>

The venn diagram for <math>\texttt{Mno(p, q, r)}</math> is shown in Figure&nbsp;1.

The venn diagram for <math>\texttt{Mno}(p, q, r)</math> is shown in Figure&nbsp;1.

{| align="center" cellpadding="8" style="text-align:center"

{| align="center" cellpadding="8" style="text-align:center"

|

|

<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>

<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>

<p><math>\text{Figure 1.}~~\texttt{Mno(p, q, r)}</math></p>

<p><math>\text{Figure 1.}~~\texttt{Mno}(p, q, r)</math></p>

|}

|}

The center cell is the region where all three arguments <math>\texttt{p, q, r}</math> hold true, so <math>\texttt{Mno(p, q, r)}</math> holds true in just the three neighboring cells.  In other words, <math>\texttt{Mno(p, q, r)} = \lnot\texttt{p}\texttt{q}\texttt{r} \lor \texttt{p}\lnot\texttt{q}\texttt{r} \lor \texttt{p}\texttt{q}\lnot\texttt{r}.</math>

The center cell is the region where all three arguments <math>p, q, r\!</math> hold true, so <math>\texttt{Mno}(p, q, r)</math> holds true in just the three neighboring cells.  In other words, <math>\texttt{Mno}(p, q, r) = \tilde{p}qr \lor p\tilde{q}r \lor pq\tilde{r}.</math>

==Initial definition==

==Initial definition==