MyWikiBiz, Author Your Legacy — Saturday September 28, 2024
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, 20:37, 9 March 2009
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| A sketch of this work is presented in the following series of Figures, where each logical proposition is expanded over the basic cells <math>\texttt{uv}, \texttt{u(v)}, \texttt{(u)v}, \texttt{(u)(v)}</math> of the 2-dimensional universe of discourse <math>U^\circ = [u, v].\!</math> | | A sketch of this work is presented in the following series of Figures, where each logical proposition is expanded over the basic cells <math>\texttt{uv}, \texttt{u(v)}, \texttt{(u)v}, \texttt{(u)(v)}</math> of the 2-dimensional universe of discourse <math>U^\circ = [u, v].\!</math> |
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− | ===Computation Summary for <math>f(u, v) = \texttt{((u)(v))}</math>=== | + | ===Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>=== |
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| Figure 1.1 is a venn diagram that show how the proposition <math>f = \texttt{((u)(v))}</math> can be expanded over the universe of discourse <math>[u, v]\!</math> to produce a logically equivalent exclusive disjunction, namely, <math>\texttt{uv~+~u(v)~+~(u)v}.</math> | | Figure 1.1 is a venn diagram that show how the proposition <math>f = \texttt{((u)(v))}</math> can be expanded over the universe of discourse <math>[u, v]\!</math> to produce a logically equivalent exclusive disjunction, namely, <math>\texttt{uv~+~u(v)~+~(u)v}.</math> |
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| </pre> | | </pre> |
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− | Figure 1.2 expands Ef = ((u + du)(v + dv)) over [u, v] to give: | + | Figure 1.2 expands <math>\operatorname{E}f = \texttt{((u + du)(v + dv))}</math> over <math>[u, v]\!</math> to give: |
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− | uv.(du dv) + u(v).(du (dv)) + (u)v.((du) dv) + (u)(v).((du)(dv)) | + | {| align="center" cellpadding="8" width="90%" |
| + | | <math>\texttt{uv~(du~dv) ~+~ u(v)~(du (dv)) ~+~ (u)v~((du) dv) ~+~ (u)(v)~((du)(dv))}</math> |
| + | |} |
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| <pre> | | <pre> |