次の集合 A,\ B について,A \cap B,A \cup B を求めよう。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\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{align*} & \begin{matrix} \colFR{black}{A} & 1 & \colBX{bisque}{$2$} & 3 & \colBX{bisque}{$4$} & 5\\ \colFR{black}{B} & & \colBX{bisque}{$2$} & & \colBX{bisque}{$4$} & & 6 & 8\\\hline & \colBX{palegreen}{$1$} & \colBX{palegreen}{$2$} & \colBX{palegreen}{$3$} & \colBX{palegreen}{$4$} & \colBX{palegreen}{$5$} & \colBX{palegreen}{$6$} & \colBX{palegreen}{$8$} \end{matrix}\\ \\ & よって\\ & A \cap B = \left\{\ \colBX{bisque}{$2,\ 4$}\ \right\}\colMM{orange}{\cdots共通部分}\\ \\ & A \cup B = \left\{\ \colBX{palegreen}{$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 8$}\ \right\}\colMM{green}{\cdots 和集合=すべて!} \end{align*} %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】
\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{align*} & \begin{matrix} \colFR{black}{A} & & 2 & \colBX{bisque}{$3$} & \colBX{bisque}{$5$} & \colBX{bisque}{$7$}\\ \colFR{black}{B} & 1 & &\colBX{bisque}{$3$} & \colBX{bisque}{$5$} & \colBX{bisque}{$7$} & 9\\\hline & \colBX{palegreen}{$1$} & \colBX{palegreen}{$2$} & \colBX{palegreen}{$3$} & \colBX{palegreen}{$5$} & \colBX{palegreen}{$7$} & \colBX{palegreen}{$9$} \end{matrix}\\ \\ & よって\\ & A \cap B = \left\{\ \colBX{bisque}{$3,\ 5,\ 7$}\ \right\}\colMM{orange}{\cdots共通部分}\\ \\ & A \cup B = \left\{\ \colBX{palegreen}{$1,\ 2,\ 3,\ 5,\ 7,\ 9$}\ \right\}\colMM{green}{\cdots 和集合=すべて!} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】
\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{align*} & \begin{matrix} \colFR{black}{A} & 1 & 2 & 3 & 4 & 5\\ \colFR{black}{B} & & & & & & 6 & 7 & 8 & 9\\\hline & \colBX{palegreen}{$1$} & \colBX{palegreen}{$2$} & \colBX{palegreen}{$3$} & \colBX{palegreen}{$4$} & \colBX{palegreen}{$5$} & \colBX{palegreen}{$6$} & \colBX{palegreen}{$7$} & \colBX{palegreen}{$8$} & \colBX{palegreen}{$9$} \end{matrix}\\ \\ & よって\\ & A \cap B = \left\{\ \colBX{bisque}{なし}\ \right\} = \varnothing\colMM{orange}{\cdots共通部分なし = 空集合}\\ \\ & A \cup B = \left\{\ \colBX{palegreen}{$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9$}\ \right\}\colMM{green}{\cdots 和集合=すべて!} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
次の集合 A,\ B,\ C について,A \cap B \cap C,A \cup B \cup C を求めよう。
【解答】
\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{align*} & \begin{matrix} \colFR{black}{A} & 1 & 2 & 3 & & \colBX{bisque}{$5$} & & \colBX{bisque}{$7$} & & \\ \colFR{black}{B} & & 2 & & 4 & \colBX{bisque}{$5$} & & \colBX{bisque}{$7$} & & 9\\ \colFR{black}{C} & & & 3 & & \colBX{bisque}{$5$} & 6 & \colBX{bisque}{$7$} & 8 & \\\hline & \colBX{palegreen}{$1$} & \colBX{palegreen}{$2$} & \colBX{palegreen}{$3$} & \colBX{palegreen}{$4$} & \colBX{palegreen}{$5$} & \colBX{palegreen}{$6$} & \colBX{palegreen}{$7$} & \colBX{palegreen}{$8$} & \colBX{palegreen}{$9$} \end{matrix}\\ \\ & よって\\ & A \cap B = \left\{\ \colBX{bisque}{$5,\ 7$}\ \right\}\colMM{orange}{\cdots共通部分}\\ \\ & A \cup B = \left\{\ \colBX{palegreen}{$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9$}\ \right\}\colMM{green}{\cdots 和集合=すべて!} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】
\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{align*} & \begin{matrix} \colFR{black}{A} & & & 3 & & \colBX{bisque}{$6$} & & 9\\ \colFR{black}{B} & 1 & 2 & 3 & & \colBX{bisque}{$6$}\\ \colFR{black}{C} & & 2 & & 4 & \colBX{bisque}{$6$} & 8\\\hline & \colBX{palegreen}{$1$} & \colBX{palegreen}{$2$} & \colBX{palegreen}{$3$} & \colBX{palegreen}{$4$} & \colBX{palegreen}{$6$} & \colBX{palegreen}{$8$} & \colBX{palegreen}{$9$} \end{matrix}\\ \\ & よって\\ & A \cap B = \left\{\ \colBX{bisque}{$6$}\ \right\}\colMM{orange}{\cdots共通部分}\\ \\ & A \cup B = \left\{\ \colBX{palegreen}{$1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 9$}\ \right\}\colMM{green}{\cdots 和集合=すべて!} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan