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, 02:38, 29 July 2011
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| 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> Wrtten in several different notations, <math>\texttt{Mno}(p) = \texttt{Not}(p) = \lnot p = \tilde{p} = p^\prime.</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> Wrtten in several different notations, <math>\texttt{Mno}(p) = \texttt{Not}(p) = \lnot p = \tilde{p} = p^\prime.</math> |
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− | 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> Expressing <math>\texttt{Mno}(p, q)</math> in terms of ands <math>(\cdot),</math> ors <math>(\lor),</math> and nots <math>(\tilde{~})</math> gives the following form: | + | 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> Expressing <math>\texttt{Mno}(p, q)</math> in terms of ands <math>(\cdot),</math> ors <math>(\lor),</math> and nots <math>(\tilde{~})</math> gives the following form. |
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| {| align="center" cellpadding="8" | | {| align="center" cellpadding="8" |
| | <math>\texttt{Mno}(p, q) = \tilde{p} \cdot q \lor p \cdot \tilde{q}.</math> | | | <math>\texttt{Mno}(p, q) = \tilde{p} \cdot q \lor p \cdot \tilde{q}.</math> |
| |} | | |} |
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| + | As usual, one omits the dots <math>(\cdot)</math> in contexts where they are understood. |
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| The venn diagram for <math>\texttt{Mno}(p, q, r)</math> is shown in Figure 1. | | The venn diagram for <math>\texttt{Mno}(p, q, r)</math> is shown in Figure 1. |