補集合の線が切れているのをつなぐ
\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*} \colMM{red}{\bf 線が切れてる} & \colMM{red}{\bf ①つなぐと}\\ \large\overline{\,A\,} \colBX{mistyrose}{$\cap$} \overline{\,B\,} &\large = \overline{A \colBX{mistyrose}{$\cup$} B}\\ \colMM{red}{\bf \Uarr ②記} & \colMM{red}{\bf 号が逆に \Uarr} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
\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*} \colMM{red}{\bf 線が切れてる} & \colMM{red}{\bf ①つなぐと}\\ \large\overline{\,A\,} \colBX{mistyrose}{$\cup$} \overline{\,B\,} &\large = \overline{A \colBX{mistyrose}{$\cap$} B}\\ \colMM{red}{\bf \Uarr ②記} & \colMM{red}{\bf 号が逆に \Uarr} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
補集合の線を切る
\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*} \colMM{red}{\bf つながってる} & \colMM{red}{\bf ①切ると}\\ \large\overline{\,A \colBX{mistyrose}{$\cap$} B\,} &\large = \overline{\,A\,} \colBX{mistyrose}{$\cup$} \overline{\,B\,}\\ \colMM{red}{\bf \Uarr ②記} & \colMM{red}{\bf 号が逆に \Uarr} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
\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*} \colMM{red}{\bf つながってる} & \colMM{red}{\bf ①切ると}\\ \large\overline{\,A \colBX{mistyrose}{$\cup$} B\,} &\large = \overline{\,A\,} \colBX{mistyrose}{$\cap$} \overline{\,B\,}\\ \colMM{red}{\bf \Uarr ②記} & \colMM{red}{\bf 号が逆に \Uarr} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
U=\left\{\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10,\ 11,\ 12\ \right\} を全体集合とする。U の部分集合
A = \left\{\ 1,\ 2,\ 3,\ 4,\ 5\ \right\}
B = \left\{\ 2,\ 4,\ 6,\ 8\ \right\}
B = \left\{\ 2,\ 4,\ 6,\ 8\ \right\}
について,次の集合を,要素を書き並べて表せ。
↓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*} \colMM{red}{\bf 線が切れてる} & \colMM{red}{\bf ①つなぐと} \\ \overline{\,A\,} \cap \overline{\,B\,} &= \overline{A \cup B}\colMM{green}{\bf \Leftarrow補集合は\ U\ から引く}\\ \colMM{red}{\bf\Uarr 記号} & \colMM{red}{\bfが逆に \Uarr}\\ &= \colBX{palegreen}{$U - $}A\cup B\\ \\ &= \left\{\ \colBX{bisque}{$1$},\ \colBX{bisque}{$2$},\ \colBX{bisque}{$3$},\ \colBX{bisque}{$4$},\ \colBX{bisque}{$5$},\ \colBX{bisque}{$6$},\ 7,\ \colBX{bisque}{$8$},\ 9,\ 10,\ 11,\ 12\ \right\}\\ & - \left\{\ \colBX{bisque}{$1$},\ \colBX{bisque}{$2$},\ \colBX{bisque}{$3$},\ \colBX{bisque}{$4$},\ \colBX{bisque}{$5$},\ \colBX{bisque}{$6$},\ \colBX{bisque}{$8$}\ \right\}\\ \\ &= \left\{\ 7,\ 9,\ 10,\ 11,\ 12\ \right\} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
U=\left\{\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\ \right\} を全体集合とする。U の部分集合
A = \left\{\ 2,\ 3,\ 5,\ 7\ \right\}
B = \left\{\ 1,\ 3,\ 5,\ 7,\ 9\ \right\}
B = \left\{\ 1,\ 3,\ 5,\ 7,\ 9\ \right\}
について,次の集合を,要素を書き並べて表せ。
↓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*} \colMM{red}{\bf 線が切れてる} & \colMM{red}{\bf ①つなぐと} \\ \overline{\,A\,} \cap \overline{\,B\,} &= \overline{A \cup B}\colMM{green}{\bf \Leftarrow補集合は\ U\ から引く}\\ \colMM{red}{\bf\Uarr 記号} & \colMM{red}{\bfが逆に \Uarr}\\ &= \colBX{palegreen}{$U - $}A\cup B\\ \\ &= \left\{\ \colBX{bisque}{$1$},\ \colBX{bisque}{$2$},\ \colBX{bisque}{$3$},\ 4,\ \colBX{bisque}{$5$},\ 6,\ \colBX{bisque}{$7$},\ 8,\ \colBX{bisque}{$9$},\ 10\ \right\}\\ & - \left\{\ \colBX{bisque}{$1$},\ \colBX{bisque}{$2$},\ \colBX{bisque}{$3$},\ \colBX{bisque}{$5$},\ \colBX{bisque}{$7$},\ \colBX{bisque}{$9$}\ \right\}\\ \\ &= \left\{\ 4,\ 6,\ 8,\ 10\ \right\} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan