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31 lines
1.1 KiB
31 lines
1.1 KiB
\begin{tabular}{|c|c|c||c|c|c||c|}
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\hline
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$p$&$q$&$r$&$\lnot p$&$r \lor \lnot p$&$q \imp p$&$\phi$\\
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\hline
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\hline
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\textbf{F} &\textbf{F} &\textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} \\
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\hline
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\textbf{F} &\textbf{F} &\textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} \\
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\hline
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\textbf{F} &\textbf{T} &\textbf{F} & \textbf{T} & \textbf{T} & \textbf{F} & \textbf{F} \\
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\hline
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\textbf{F} &\textbf{T} &\textbf{T} & \textbf{T} & \textbf{T} & \textbf{F} & \textbf{F} \\
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\hline
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\textbf{T} &\textbf{F} &\textbf{F} & \textbf{F} & \textbf{F} & \textbf{T} & \textbf{F} \\
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\hline
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\textbf{T} &\textbf{F} &\textbf{T} & \textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} \\
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\hline
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\textbf{T} &\textbf{T} &\textbf{F} & \textbf{F} & \textbf{F} & \textbf{T} & \textbf{F} \\
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\hline
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\textbf{T} &\textbf{T} &\textbf{T} & \textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} \\
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\hline
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\end{tabular}
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\begin{equation*}
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\begin{split}
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\textit{DNF}(\phi) = & (\lnot p \land \lnot q \land \lnot r) \\
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\lor & (\lnot p \land \lnot q \land r) \\
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\lor & (p \land \lnot q \land r) \\
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\lor & (p \land q \land r) \\
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\end{split}
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\end{equation*}
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