MyWikiBiz, Author Your Legacy — Monday November 25, 2024
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, 20:44, 1 May 2009
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| Interpreting the formula <math>\mathit{l}^\mathrm{w}\!</math> as <math>\mathrm{J} ~\text{loves}~ \mathrm{K} ~\Leftarrow~ \mathrm{K} ~\text{is a woman}</math> highlights the form of the converse implication inherent in it, and this in turn reveals the analogy between implication and involution that accounts for the aptness of the latter name. | | Interpreting the formula <math>\mathit{l}^\mathrm{w}\!</math> as <math>\mathrm{J} ~\text{loves}~ \mathrm{K} ~\Leftarrow~ \mathrm{K} ~\text{is a woman}</math> highlights the form of the converse implication inherent in it, and this in turn reveals the analogy between implication and involution that accounts for the aptness of the latter name. |
| + | |
| + | The operations of the forms <math>x^y = z\!</math> and <math>(x\!\Leftarrow\!y) = z</math> for <math>x, y, z \in \mathbb{B} = \{ 0, 1 \}</math> are tabulated below: |
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| {| align="center" cellspacing="6" width="90%" | | {| align="center" cellspacing="6" width="90%" |
| | | | | |
| <math> | | <math> |
− | \begin{bmatrix} | + | \begin{matrix} |
| 0^0 & = & 1 | | 0^0 & = & 1 |
| \\ | | \\ |
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| \\ | | \\ |
| 1^1 & = & 1 | | 1^1 & = & 1 |
− | \end{bmatrix} | + | \end{matrix} |
| \qquad\qquad\qquad | | \qquad\qquad\qquad |
− | \begin{bmatrix} | + | \begin{matrix} |
| 0\!\Leftarrow\!0 & = & 1 | | 0\!\Leftarrow\!0 & = & 1 |
| \\ | | \\ |
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| \\ | | \\ |
| 1\!\Leftarrow\!1 & = & 1 | | 1\!\Leftarrow\!1 & = & 1 |
− | \end{bmatrix} | + | \end{matrix} |
| </math> | | </math> |
| |} | | |} |