次の命題の真偽を調べよ。また,その命題の逆,裏,対偶を述べて,その真偽を調べよ。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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