\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 和集合} } & \colMM{red}{\ は A たす B ひく {\bf 共通部分}}\\
n(A \cup B) &= n(A)+n(B)-n(A \cap B)\\
\\
とくに， \ \\
n(A \cup B) =&\varnothing のとき\colMM{red}{ n(A \cap B)=0}\\
n(A \cup B) &= n(A)+n(B)\colNS{lightgray}{-n(A \cap B)}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{\normalsize#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 補集合}\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく\ {\bf 元の集合}}\\
n(\overline{\,A\,}) &= n(U)-n(A)\\
& \colMM{red}{ バーを取る！\Uarr}\\
\\
\colMM{red}{{\bf 補集合 }\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく {\bf 元の集合}}\\
n(\overline{\,\colBX{bisque}{集合の式}\,}) &= n(U)-n(\colBX{bisque}{集合の式})\\
& \colMM{red}{ バーを取る！\Uarr}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan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集合 A,\ B が全体集合 U の部分集合で，
n(U)=40,\ n(A)=23,
n(B)=15,\ n(A \cap B)=3
であるとき，次の集合の要素の個数を求めよ。
↓この問題へのリンクはこちら（右クリックで保存）
【解答】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\Kotae{35}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 和集合} } & \colMM{red}{\ \ は A \ \ たす B ひく {\bf 共通部分}}\\
n(A \cup B) &= \colBX{bisque}{$n(A)$}+\colBX{palegreen}{$n(B)$}-\colBX{violet}{$n(A \cap B)$}\\
\\
&= \colBX{bisque}{$\nA$}+\colBX{palegreen}{$\nB$}-\colBX{violet}{$\nAcapB$}\\
\\
&= \Kotae
\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】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\Kotae{17}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合}\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく\ {\bf 元の集合}}\\
n(\overline{\,A\,}) &= n(U) - \colBX{bisque}{$n(A)$}\\
& \colMM{red}{ \ バーを取る！\Uarr}\\
&= \nU-\colBX{bisque}{$\nA$}\\
\\
&= \Kotae
\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】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\Kotae{25}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合}\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく\ {\bf 元の集合}}\\
n(\overline{\,B\,}) &= n(U) - \colBX{bisque}{$n(B)$}\\
& \colMM{red}{ \ バーを取る！\Uarr}\\
&= \nU-\colBX{bisque}{$\nB$}\\
\\
&= \Kotae
\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】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\nAcupB{35}
\def\Kotae{5}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合 }\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく {\bf 元の集合}}\\
n(\overline{\,A \cup B\,}) &= n(U) - \colBX{bisque}{$n(A \cup B)$} \colMM{orange}{{\bf 和集合}は}\\
& \colMM{orange}{ A \ たす B \ ひく {\bf 共通部分}}\\
&= \nU-\left\{\colBX{bisque}{$n(A)+n(B)-n(A \cap B)$}\right\}\\
\\
&= \nU-\{\nA+\nB-\nAcapB\}\\
\\
&= \nU-\nAcupB\\
\\
&= \Kotae
\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】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\nAcupB{35}
\def\Kotae{37}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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}\\
n(\overline{\,A\,} \cup \overline{\,B\,}) &= n(\overline{\,A \cap B\,}) \colMM{orange}{{\bf 補集合}は}\\
\colMM{red}{\bf \Uarr ②\ 記} & \colMM{red}{\bf 号が逆に\ \Uarr}\\
&= n(U) - \colBX{bisque}{$n(A \cap B)$}\\
& \colMM{orange}{ 全体 ひく {\bf 元の集合}}\\
&= \nU-\nAcapB\\
\\
&= \Kotae
\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】
\def\nU{40}
\def\nA{23}
\def\nB{15}
\def\nAcapB{3}
\def\nAcupB{35}
\def\Kotae{37}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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}\\
n(\overline{\,A\,} \cup \overline{\,B\,}) &= n(\overline{\,A \cap B\,}) \colMM{orange}{{\bf 補集合}は}\\
\colMM{red}{\bf \Uarr ②\ 記} & \colMM{red}{\bf 号が逆に\ \Uarr}\\
&= n(U) - \colBX{bisque}{$n(A \cap B)$}\\
& \colMM{orange}{ 全体 ひく {\bf 元の集合}}\\
&= \nU-\nAcapB\\
\\
&= \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan集合 A,\ B が全体集合 U の部分集合で，
n(U)=20,\ n(A)=13,
n(B)=9,\ n(A \cap B)=5
であるとき，次の集合の要素の個数を求めよ。
↓この問題へのリンクはこちら（右クリックで保存）
【解答】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\Kotae{17}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 和集合} } & \colMM{red}{\ \ は A \ \ たす B ひく {\bf 共通部分}}\\
n(A \cup B) &= \colBX{bisque}{$n(A)$}+\colBX{palegreen}{$n(B)$}-\colBX{violet}{$n(A \cap B)$}\\
\\
&= \colBX{bisque}{$\nA$}+\colBX{palegreen}{$\nB$}-\colBX{violet}{$\nAcapB$}\\
\\
&= \Kotae
\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】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\Kotae{7}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合}\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく\ {\bf 元の集合}}\\
n(\overline{\,A\,}) &= n(U) - \colBX{bisque}{$n(A)$}\\
& \colMM{red}{ \ バーを取る！\Uarr}\\
&= \nU-\colBX{bisque}{$\nA$}\\
\\
&= \Kotae
\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】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\Kotae{11}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合}\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく\ {\bf 元の集合}}\\
n(\overline{\,B\,}) &= n(U) - \colBX{bisque}{$n(B)$}\\
& \colMM{red}{ \ バーを取る！\Uarr}\\
&= \nU-\colBX{bisque}{$\nB$}\\
\\
&= \Kotae
\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】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\nAcupB{17}
\def\Kotae{3}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合 }\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく {\bf 元の集合}}\\
n(\overline{\,A \cup B\,}) &= n(U) - \colBX{bisque}{$n(A \cup B)$} \colMM{orange}{{\bf 和集合}は}\\
& \colMM{orange}{ A \ たす B \ ひく {\bf 共通部分}}\\
&= \nU-\left\{\colBX{bisque}{$n(A)+n(B)-n(A \cap B)$}\right\}\\
\\
&= \nU-\{\nA+\nB-\nAcapB\}\\
\\
&= \nU-\nAcupB\\
\\
&= \Kotae
\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】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\nAcupB{17}
\def\Kotae{15}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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}\\
n(\overline{\,A\,} \cup \overline{\,B\,}) &= n(\overline{\,A \cap B\,}) \colMM{orange}{{\bf 補集合}は}\\
\colMM{red}{\bf \Uarr ②\ 記} & \colMM{red}{\bf 号が逆に\ \Uarr}\\
&= n(U) - \colBX{bisque}{$n(A \cap B)$}\\
& \colMM{orange}{ 全体 ひく {\bf 元の集合}}\\
&= \nU-\nAcapB\\
\\
&= \Kotae
\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】
\def\nU{20}
\def\nA{13}
\def\nB{9}
\def\nAcapB{5}
\def\nAcupB{17}
\def\Kotae{15}
%
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\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 補集合 }\ } & \colMM{red}{\ \ は\ \ \ 全体\ \ ひく {\bf 元の集合}}\\
n(\overline{\,A \cap B\,}) &= n(U) - \colBX{bisque}{$n(A \cap B)$}\\
\\
&= \nU-\nAcapB\\
\\
&= \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan