命題の逆・対偶・裏を求める

\def\sikil{x=-2}\def\sikilh{x \neq -2}
\def\sikir{x^2=4}\def\sikirh{x^2 \neq 4}
\def\tfb{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　x=2）}}
\def\tfa{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$} \tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{x^2=x}\def\sikilh{x^2 \neq x}
\def\sikir{x=1}\def\sikirh{x \neq 1}
\def\tfa{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　x=0）}}
\def\tfb{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{\small n\ は12の倍数}\def\sikilh{\small n\ は12の倍数ではない}
\def\sikir{\small n\ は6の倍数}\def\sikirh{\small n\ は6の倍数ではない}
\def\tfa{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　n=12）}}
\def\tfb{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{a=b}\def\sikilh{a \neq b}
\def\sikir{ac=bc}\def\sikirh{ac \neq bc}
\def\tfb{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　a=2,b=3,c=0）}}
\def\tfa{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{x=0\ または\ y=0}\def\sikilh{x \neq 0\ かつ\ y \neq 0}
\def\sikir{xy=0}\def\sikirh{xy \neq 0}
\def\tfa{ & \colFR{red}{真}}
\def\tfb{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{x=0\ かつ\ y=0}\def\sikilh{x \neq 0\ または\ y \neq 0}
\def\sikir{x+y=0}\def\sikirh{x+y \neq 0}
\def\tfb{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　x=2,y=-2）}}
\def\tfa{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\sikil{x=0\ かつ\ y=0}\def\sikilh{x \neq 0\ または\ y \neq 0}
\def\sikir{x+y=0}\def\sikirh{x+y \neq 0}
\def\tfb{ & &  \colFR{blue}{偽} & \colMM{blue}{（反例　x=2,y=-2）}}
\def\tfa{ & \colFR{red}{真}}
\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{matrix}
\colFR{red}{\bf 命題} & \colBX{bisque}{$\sikil$} & \Longrightarrow & \colBX{palegreen}{$\sikir$} \tfa\\
& \colMM{orange}{後ろに\ \rightarrow} & & \colMM{green}{\leftarrow前に}\\
逆 & \colBX{palegreen}{$\sikir$} & \Longrightarrow & \colBX{bisque}{$\sikil$} \tfb\\
& \colMM{green}{\Darr 否定} & & \colMM{orange}{\Darr 否定}\\
\colFR{red}{\bf 対偶} & \colBX{palegreen}{$\sikirh$} & \Longrightarrow & \colBX{bisque}{$\sikilh$} \tfa\\
& \colMM{green}{後ろに\ \rightarrow} & & \colMM{orange}{\leftarrow前に}\\
裏 & \colBX{bisque}{$\sikilh$} & \Longrightarrow & \colBX{palegreen}{$\sikirh$}\tfb
\end{matrix}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan