犹ｶﾄ犧金ｸ歩ｸ歩ｸ歩ｸ歩ｸ歩ｸ
- 1. 犧ｪ犧｣犧ｸ犧巵ｹ犧吭ｸｷ犹霞ｸｭ犧ｫ犧ｲ犧ｧ犧ｴ犧癌ｸｲ 犹ｶﾄ犧金ｸ 犧吭ｸｴ犧｢犧ｲ犧｡ : 犹ｶﾄ犧金ｸ歩ｹ犧幢恍犧吭ｸｭ犧吭ｸｴ犧｢犧ｲ犧｡ 犧犧ｷ犧ｭ 犹犧｡怺犧｡犧ｵ犧吭ｸｴ犧｢犧ｲ犧｡犧吭ｸｱ犹謂ｸ吭ｹ犧ｭ犧 犹犧｡犧ｷ犹謂ｸｭ犧樅ｸｹ犧扉ｸ籾ｸｶ犧 犹ｶﾄ犧金ｸ 犹犧ｫ恚犧吭ｸｶ犧≒ｸ籾ｸｶ犧 窶杳ｸ≒ｸ･犧ｸ怺犧｡窶 犧金ｸｶ犹謂ｸ犧≒ｸ･犧ｸ怺犧｡犧吭ｸｱ犹霞ｸ吭ｸｭ犧ｲ犧謂ｸ謂ｸｰ犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧 犧ｫ犧｣犧ｷ犧ｭ犹犧｡怺犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ≒ｹ犹犧費恚 犧ｪ犹財ｸｲ犧ｫ犧｣犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸ金ｸｶ犹謂ｸ犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧 犧ｪ犧ｲ犧｡犧ｲ犧｣犧籾ｹ≒ｸ夲怺犧犹犧費恚犹犧幢恍犧 2 犧巵ｸ｣犧ｰ犹犧犧 犧犧ｷ犧ｭ 犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ｡犧ｵ犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸ伶ｸｵ犹謂ｹ≒ｸ呻怺犧吭ｸｭ犧 --> 犹犧｣犧ｲ犹犧｣犧ｵ犧｢犧≒ｹｶﾄ犧金ｸ歩ｸ吭ｸｱ犹霞ｸ吭ｸｧ怺犧ｲ 窶憫ｹｶﾄ犧金ｸ歩ｸ謂ｹ財ｸｲ犧≒ｸｱ犧披 犧ｫ犧ｲ犧 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ｡犧ｵ犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸ｡犧ｲ犧≒ｸ｡犧ｲ犧｢犹犧｡怺犧ｪ犧ｲ犧｡犧ｲ犧｣犧籾ｸ壟ｸｭ犧≒ｸ巵ｸ｣犧ｴ犧｡犧ｲ犧内ｸ伶ｸｵ犹謂ｹ≒ｸ呻怺犧吭ｸｭ犧吭ｹ犧費恚犹犧｣犧ｲ犹犧｣犧ｵ犧｢犧 窶憫ｹｶﾄ犧金ｸ歩ｸｭ犧吭ｸｱ犧吭ｸ包恷窶 犧≒ｸｲ犧｣犹犧もｸｵ犧｢犧吭ｹｶﾄ犧金ｸ 犧吭ｸｴ犧｢犧｡犧伶ｹ財ｸｲ犧≒ｸｱ犧 2 犧ｧ犧ｴ犧倨ｸｵ 犧犧ｷ犧ｭ 1. 犹≒ｸ壟ｸ壟ｹ≒ｸ謂ｸ≒ｹ≒ｸ謂ｸ犧ｪ犧｡犧ｲ犧癌ｸｴ犧, 2. 犹≒ｸ壟ｸ壟ｸ壟ｸｭ犧≒ｹ犧犧ｷ犹謂ｸｭ犧吭ｹ犧 犧. 犹≒ｸ壟ｸ壟ｹ≒ｸ謂ｸ≒ｹ≒ｸ謂ｸ犧ｪ犧｡犧ｲ犧癌ｸｴ犧 犹犧奇怺犧 A = {1, 2,3} 犧ｭ怺犧ｲ犧吭ｸｧ怺犧ｲ A 犹犧幢恍犧吭ｹｶﾄ犧金ｸ歩ｸ金ｸｶ犹謂ｸ犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧幢恍犧 1, 2 犹≒ｸ･犧ｰ 3 犧. 犹≒ｸ壟ｸ壟ｸ壟ｸｭ犧≒ｹ犧犧ｷ犹謂ｸｭ犧吭ｹ犧 犹犧奇怺犧 A = { x 竏 I + 4 < x < 6} 犧ｭ怺犧ｲ犧吭ｸｧ怺犧ｲ A 犹犧幢恍犧吭ｹｶﾄ犧金ｸ歩ｸもｸｭ犧 x 犧金ｸｶ犹謂ｸ x 犹犧幢恍犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡犧壟ｸｧ犧 犹もｸ扉ｸ｢犧伶ｸｵ犹 x 犧｡犧ｵ犧犧ｲ犧｡犧ｲ犧≒ｸ≒ｸｧ怺犧ｲ 4 犹≒ｸ包怺犧呻恚犧ｭ犧｢犧≒ｸｧ怺犧ｲ 6 怺 犧金ｸｶ犹謂ｸ 犹犧｣犧ｲ犧ｪ犧ｲ犧｡犧ｲ犧｣犧籾ｸ伶ｸｵ犹謂ｸ謂ｸｰ犹犧もｸｵ犧｢犧吭ｹ≒ｸ伶ｸ吭ｹｶﾄ犧金ｸ A 犹犧費恚犧費恚犧ｧ犧｢犧≒ｸｲ犧｣犹≒ｸ謂ｸ≒ｹ≒ｸ謂ｸ犧ｪ犧｡犧ｲ犧癌ｸｴ犧 犧犧ｷ犧ｭ A ={5} 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷犧伶ｸｵ犹謂ｹ犧奇恚犹犧吭ｹｶﾄ犧金ｸ 1. 竏 犹≒ｸ伶ｸ 犹犧幢恍犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧 犹犧奇怺犧 2 竏 I+ 犧ｭ怺犧ｲ犧吭ｸｧ怺犧ｲ 2 犹犧幢恍犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡犧壟ｸｧ犧 2. U 犹≒ｸ伶ｸ 犹犧ｭ犧≒ｸ犧樅ｸｪ犧ｱ犧｡犧樅ｸｱ犧伶ｸ假恷 犹犧奇恚犹犧樅ｸｷ犹謂ｸｭ犧≒ｹ財ｸｲ犧ｫ犧吭ｸ扉ｸもｸｭ犧壟ｹ犧もｸ歩ｸもｸｭ犧犧ｪ犧ｴ犹謂ｸ犧伶ｸｵ犹謂ｹ犧｣犧ｲ犧ｪ犧吭ｹ犧謂ｹ≒ｸ･犧ｰ犧≒ｹ財ｸｲ犧･犧ｱ犧犧ｨ犧ｶ犧≒ｸｩ犧ｲ 3. 竏,{ } 犹≒ｸ伶ｸ 犹ｶﾄ犧金ｸ歩ｸｧ怺犧ｲ犧 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷犧もｸｭ犧犧｣犧ｰ犧壟ｸ壟ｸ謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸ伶ｸｵ犹謂ｸ樅ｸ壟ｸ夲怺犧ｭ犧｢ R : 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸ謂ｸ｣犧ｴ犧 Q : 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸ歩ｸ｣犧｣犧≒ｸ｢犧ｰ Q窶 : 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｭ犧歩ｸ｣犧｣犧≒ｸ｢犧ｰ I: 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡ 犹犧ｨ犧ｩ犧ｪ怺犧ｧ犧 犧伶ｸｨ犧吭ｸｴ犧｢犧｡犧金ｹ霞ｹ財ｸｲ I-: 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡犧･犧 I0: 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡ 0 I+: 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｹ犧歩ｹ犧｡犧壟ｸｧ犧 犧≒ｸｲ犧｣犹犧暦怺犧ｲ犧≒ｸｱ犧吭ｸもｸｭ犧犹ｶﾄ犧金ｸ 1. 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧暦怺犧ｲ犧≒ｸｱ犧 2. 犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧ｫ犧｡犧ｷ犧ｭ犧吭ｸ≒ｸｱ犧 犧≒ｸｲ犧｣犹犧伶ｸｵ犧｢犧壟ｹ犧暦怺犧ｲ犧≒ｸｱ犧吭ｸもｸｭ犧犹ｶﾄ犧金ｸ 1. 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧暦怺犧ｲ犧≒ｸｱ犧 犧≒ｸｲ犧｣犧≒ｹ財ｸｲ犧ｫ犧吭ｸ扉ｹｶﾄ犧金ｸ 犧謂ｸｰ犧包恚犧ｭ犧 1.) 犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ≒ｸ呻怺犧吭ｸｭ犧 犧ｫ犧｣犧ｷ犧ｭ 犹犧｡怺犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧･犧｢ 2.) 犧ｫ犧ｲ犧≒ｸ≒ｹ財ｸｲ犧ｫ犧吭ｸ扉ｹ犧幢恍犧吭ｹ≒ｸ壟ｸ壟ｸ壟ｸ≒ｹ犧犧ｷ犹謂ｸｭ犧吭ｹ犧 犧謂ｸｰ犧包恚犧ｭ犧犹犧｡怺犧≒ｹ財ｸｲ犧≒ｸｧ犧｡ 犧犧ｷ犧ｭ 犧伶ｸｸ犧≒ｸ犧吭ｸ包恚犧ｭ犧犧歩ｸｭ犧壟ｹ犧ｫ犧｡犧ｷ犧ｭ犧吭ｸ≒ｸｱ犧 犧歩ｸｱ犧ｧ犧ｭ犧｢怺犧ｲ犧犧もｸｭ犧犧≒ｸｲ犧｣犧≒ｹ財ｸｲ犧ｫ犧吭ｸ扉ｹｶﾄ犧金ｸ歩ｸ伶ｸｵ犹謂ｹ犧｡怺犧籾ｸｹ犧≒ｸ包恚犧ｭ犧 犹犧ｫ恚犹ｶﾄ犧金ｸ A 犹≒ｸ伶ｸ吭ｹｶﾄ犧金ｸ歩ｸもｸｭ犧犧犧吭ｸ伶ｸｵ犹謂ｸｫ犧･怺犧ｭ犧伶ｸｵ犹謂ｸｪ犧ｸ犧扉ｹ犧吭ｹもｸ｣犧犹犧｣犧ｵ犧｢犧 犹犧幢恍犧吭ｸ包恚犧
- 2. 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷 竓 A 竓 B 犧ｭ怺犧ｲ犧吭ｸｧ怺犧ｲ 窶廣 犹犧幢恍犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸもｸｭ犧 B窶 犧吭ｸｴ犧｢犧ｲ犧｡ : A 犧謂ｸｰ犹犧幢恍犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸもｸｭ犧 B 犹犧費恚 犧≒ｹ犧包怺犧ｭ犹犧｡犧ｷ犹謂ｸｭ 犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ伶ｸｸ犧≒ｸ歩ｸｱ犧ｧ犹犧吭ｹｶﾄ犧金ｸ A 犧包恚犧ｭ犧犧ｭ犧｢犧ｹ怺犹犧吭ｹｶﾄ犧金ｸ B 犧ゑ恚犧ｭ犧犧ｧ犧｣犧謂ｹ財ｸｲ : 犹ｶﾄ犧金ｸ歩ｸｧ怺犧ｲ犧犹犧幢恍犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸもｸｭ犧犧伶ｸｸ犧≒ｹｶﾄ犧金ｸ 犧歩ｸｱ犧ｧ犧ｭ犧｢怺犧ｲ犧犧≒ｸｲ犧｣犧ｫ犧ｲ犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ 犧歩ｸ｢.1 犧謂ｸ犧ｫ犧ｲ犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸ伶ｸｵ犹謂ｹ犧幢恍犧吭ｹ犧巵ｹ犧費恚犧伶ｸｱ犹霞ｸ犧ｫ犧｡犧扉ｸもｸｭ犧 A 犹犧｡犧ｷ犹謂ｸｭ A = {1, 2} 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ A = 竏 , {1}, {2}, {1,2} 犧謂ｸｰ犧ｪ犧ｱ犧犹犧≒ｸ歩ｹ犧費恚犧ｧ怺犧ｲ 犹≒ｸ包怺犧･犧ｰ犹ｶﾄ犧金ｸ歩ｸもｸｭ犧犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ A 犹犧奇怺犧 {1} 犧｡犧ｵ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸｫ犧吭ｸｶ犹謂ｸ犧歩ｸｱ犧ｧ 犧犧ｷ犧ｭ 1 犧金ｸｶ犹謂ｸ犧≒ｹ犹犧幢恍犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧 A 犧費恚犧ｧ犧｢犹犧奇怺犧吭ｸ≒ｸｱ犧 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸもｸｭ犧 A 犧｡犧ｵ犧伶ｸｱ犹霞ｸ犧ｫ犧｡犧 4 犹ｶﾄ犧金ｸ 犧歩ｸ｢.2 犧謂ｸ犧ｫ犧ｲ犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸ伶ｸｵ犹謂ｹ犧幢恍犧吭ｹ犧巵ｹ犧費恚犧伶ｸｱ犹霞ｸ犧ｫ犧｡犧扉ｸもｸｭ犧 B 犹犧｡犧ｷ犹謂ｸｭ B = {3, 4, 5} 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ B = 竏 , {3}, {4}, {5}, {3,4}, {3,5}, {4,5}, {3,4,5} 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸもｸｭ犧 B 犧｡犧ｵ犧伶ｸｱ犹霞ｸ犧ｫ犧｡犧 8 犹ｶﾄ犧金ｸ 犧謂ｸｲ犧 犧歩ｸ｢.1 犹≒ｸ･犧ｰ 犧歩ｸ｢.2 犧謂ｸｰ犧ｪ犧ｲ犧｡犧ｲ犧｣犧籾ｸｪ犧ｱ犧犹犧≒ｸ歩ｹ犧費恚犧ｧ怺犧ｲ 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸ｡犧ｵ犧犧ｧ犧ｲ犧｡犧ｪ犧ｱ犧｡犧樅ｸｱ犧吭ｸ假恷犧≒ｸｱ犧壟ｸ謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犹ｶﾄ犧金ｸ歩ｹ犧扉ｸｴ犧｡犧犧ｷ犧ｭ 犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧ｱ犧壟ｹｶﾄ犧金ｸ = 2 犧｢犧≒ｸ≒ｹ財ｸｲ犧･犧ｱ犧犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犹ｶﾄ犧金ｸ歩ｹ犧扉ｸｴ犧｡ = 2n 犹犧｡犧ｷ犹謂ｸｭ n 犧犧ｷ犧ｭ犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犹ｶﾄ犧金ｸ歩ｹ犧扉ｸｴ犧｡ 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｹ≒ｸ暦恚 犧犧ｷ犧ｭ犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｸ伶ｸｵ犹謂ｹ犧｡怺犹犧奇怺犹ｶﾄ犧金ｸ歩ｹ犧扉ｸｴ犧｡ 犹犧奇怺犧 A = {1, 2} 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ A = 竏 , {1}, {2}, {1,2} 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｹ≒ｸ暦恚 犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ歩ｹ犧｡怺犹≒ｸ暦恚 犧≒ｸｲ犧｣ Operation 犧もｸｭ犧犹ｶﾄ犧金ｸ 1. Union : 犧｣犧ｧ犧｡ -> 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷 竏ｪ 2. Intersection : 犹犧ｫ犧｡犧ｷ犧ｭ犧 -> 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷 竏ｩ 3. Difference : 犧包怺犧ｲ犧 -> 犧･犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷 - 4. Complement : 犹犧｡怺犹犧ｭ犧ｲ -> 犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷 窶 犧歩ｸｱ犧ｧ犧ｭ犧｢怺犧ｲ犧犧≒ｸｲ犧｣犹犧奇恚犧犧ｲ犧 U = {1, 2, 3, 4, 窶ｦ, 10}, A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8, 10} 1. Union : A 竏ｪ B = {1, 2, 3, 4, 5, 6, 8, 10} ; B 竏ｪ A = {1, 2, 3, 4, 5, 6, 8, 10} -> A 竏ｪ B = B 竏ｪ A 2. Intersection : A 竏ｩ B = {2, 4} ; B 竏ｩ A = {2, 4} -> A 竏ｩ B = B 竏ｩ A 3. Difference : A - B = {1, 3, 5} ; B 窶 A = {6, 8, 10} -> A 窶 B 竕 B 窶 A 犧謂ｹ財ｸｲ犧怺犧ｲ犧｢ 犹 犧ｧ怺犧ｲ : 犹犧幢恍犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ伶ｸｵ犹謂ｸｭ犧｢犧ｹ怺犹犧霞ｸ樅ｸｲ犧ｰ犹犧吭ｹｶﾄ犧金ｸ歩ｸｫ犧呻恚犧ｲ 犹犧｡怺犧ｭ犧｢犧ｹ怺犹犧吭ｹｶﾄ犧金ｸ歩ｸｫ犧･犧ｱ犧 4. Complement : A窶 = {6, 7, 8, 9, 10} ; B窶 = {1, 3, 5, 7, 9} 犹犧｡怺犹犧ｭ犧ｲ犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｹ犧吭ｹｶﾄ犧金ｸ歩ｸ伶ｸｵ犹謂ｸ｡犧ｵ犹犧犧｣犧ｷ犹謂ｸｭ犧犧ｫ犧｡犧ｲ犧｢ 窶 犹≒ｸ包怺犧ｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸ伶ｸｵ犹謂ｹ犧費恚犧｢犧ｱ犧犧犧犧包恚犧ｭ犧犧ｭ犧｢犧ｹ怺犹犧 U 犧ｪ犧｡犧壟ｸｱ犧歩ｸｴ犧もｸｭ犧犧≒ｸｲ犧｣ Operation 1. A 竏ｪ B = B 竏ｪ A 犧≒ｸｲ犧｣犧ｪ犧･犧ｱ犧壟ｸ伶ｸｵ犹 2. A 竏ｩ B = B 竏ｩ A 3. A 竏ｪ 竏 = A 4. A 竏ｩ 竏 = 竏 犹犧ｭ犧≒ｸ･犧ｱ犧≒ｸｩ犧難恷 5. A 竏ｪ U = U 6. A 竏ｩ U = A 7. A 竏ｪ (B 竏ｪ C) = (A 竏ｪ B) 竏ｪ C 犧≒ｸｲ犧｣犹犧巵ｸ･犧ｵ犹謂ｸ｢犧吭ｸ≒ｸ･犧ｸ怺犧｡ 8. A 竏ｩ (B 竏ｩ C) = (A 竏ｩ B) 竏ｩ C
- 3. 9. A 竏ｪ (B 竏ｩ C) = (A 竏ｪ B) 竏ｩ (A 竏ｪ C) 10. A 竏ｩ (B 竏ｪ C) = (A 竏ｩ B) 竏ｪ (A 竏ｩ C) 犧≒ｸｲ犧｣犧≒ｸ｣犧ｰ犧謂ｸｲ犧｢ 11. A 窶 (B 竏ｩ C) = (A 窶 B) 竏ｩ (A 窶 C) 12. A 窶 (B 竏ｪ C) = (A 窶 B) 竏ｪ (A 窶 C) 13. (A窶)窶 = A 14. (A 竏ｪ B)窶 = A窶 竏ｩ B窶 犧ｪ犧｡犧壟ｸｱ犧歩ｸｴ犧もｸｭ犧 Complement 15. A 竏ｪ A窶 = U 16. A 竏ｩ A窶 = 竏 17. **A - B = A 竏ｩ B窶 = B窶 窶 A窶 ** Difference 18. A 窶 B 竕 B 窶 A 犹犧樅ｸｲ犹犧ｧ犧ｭ犧｣恷犹ｶﾄ犧金ｸ (Power Set) 犧犧ｷ犧ｭ 犹ｶﾄ犧金ｸ歩ｸもｸｭ犧犧ｪ犧ｱ犧壟ｹｶﾄ犧金ｸ 犹犧奇怺犧 A = {1, 2} -> Subset A = 竏 , {1}, {2}, {1, 2} Power Set A = { 竏 , {1}, {2}, {1, 2}} 犧犧ｧ犧ｲ犧｡犧ｪ犧ｱ犧｡犧樅ｸｱ犧吭ｸ假恷犧もｸｭ犧 Power Set 犧≒ｸｱ犧壟ｸ≒ｸｲ犧｣ Operation P(A 竏ｩ B) = P(A) 竏ｩ P(B) P(A 竏ｪ B) 竕 P(A) 竏ｪ P(B) 犧厄恚犧ｲ A 竓 B 犹≒ｸ･恚犧ｧ P(A 竏ｪ B) = P(A) 竏ｪ P(B) -> 犧扉ｸｱ犧犧吭ｸｱ犹霞ｸ吭ｸｪ犧ｲ犧｡犧ｲ犧｣犧籾ｸｪ犧｣犧ｸ犧巵ｹ犧費恚犧ｧ怺犧ｲ P(A) 竏ｪ P(B) 竓 P(A 竏ｪ B) P(A 窶 B) 竕 P(A) 窶 P(B) 犹≒ｸ憫ｸ吭ｸ犧ｲ犧樅ｹ犧ｧ犧吭ｸ呻恷 窶 犧ｭ犧ｭ犧｢犹犧･犧ｭ犧｣恷 犹犧幢恍犧吭ｹ≒ｸ憫ｸ吭ｸ犧ｲ犧樅ｸｫ犧｣犧ｷ犧ｭ犧ｪ犧ｱ犧財ｸ･犧ｱ犧≒ｸｩ犧難恷犹≒ｸ伶ｸ吭ｸ≒ｸｲ犧｣犹≒ｸ謂ｸ≒ｹ≒ｸ謂ｸ 犧巵ｸ｣犧ｰ犹もｸ｢犧癌ｸ呻恷 犧犧ｷ犧ｭ 犧伶ｹ財ｸｲ犹犧ｫ恚犧怺犧ｲ犧｢犧包怺犧ｭ犧≒ｸｲ犧｣犧伶ｹ財ｸｲ犧犧ｧ犧ｲ犧｡犹犧ゑ恚犧ｲ犹犧謂ｹ≒ｸ･犧ｰ犧≒ｸｲ犧｣犧犹財ｸｲ犧吭ｸｧ犧 犹≒ｸ伶ｸ U 犹犧ｭ犧≒ｸ犧樅ｸｪ犧ｱ犧｡犧樅ｸｱ犧伶ｸ假恷犧費恚犧ｧ犧｢ 犧≒ｸ｣犧ｭ犧壟ｸｪ犧ｵ犹謂ｹ犧ｫ犧･犧ｵ犹謂ｸ｢犧｡ 犹≒ｸ伶ｸ吭ｹｶﾄ犧金ｸ歩ｸ包怺犧ｲ犧 犹 犧費恚犧ｧ犧｢犧ｧ犧犧≒ｸ･犧｡犹犧吭ｸ≒ｸ｣犧ｭ犧 犧≒ｸｲ犧｣犧ｫ犧ｲ犧謂ｹ財ｸｲ犧吭ｸｧ犧吭ｸｪ犧｡犧ｲ犧癌ｸｴ犧≒ｸもｸｭ犧犹ｶﾄ犧金ｸ 犧ｪ犧ｲ犧｡犧ｲ犧｣犧籾ｸ樅ｸｴ犧ｪ犧ｹ犧謂ｸ呻恷犹犧費恚犧謂ｸｲ犧≒ｸ≒ｸｲ犧｣犹犧もｸｵ犧｢犧吭ｹ≒ｸ憫ｸ吭ｸ犧ｲ犧樅ｹ犧ｧ犧吭ｸ呻恷 窶 犧ｭ犧ｭ犧｢犹犧･犧ｭ犧｣恷 n(A 竏ｪ B) = n(A) + n(B) 窶 n(A 竏ｩ B) n(A 竏ｪ B 竏ｪ C) = n(A) + n(B) + n(C) 窶 n(A 竏ｩ B) 窶 n(A 竏ｩ C) 窶 n(B 竏ｩ C) + n(A 竏ｩ B 竏ｩ C) 犧ｪ犹財ｸｲ犧ｫ犧｣犧ｱ犧壟ｹ犧吭ｸｷ犹霞ｸｭ犧ｫ犧ｲ犹犧吭ｹ犧｣犧ｷ犹謂ｸｭ犧犹ｶﾄ犧金ｸ 犧ｪ犧｣犧ｸ犧巵ｸ犧｣怺犧ｲ犧ｧ 犹 犹犧費恚犧扉ｸｱ犧犹≒ｸｪ犧扉ｸ犹犧ｧ恚犧費恚犧ｲ犧吭ｸ壟ｸ 犧包怺犧ｭ犧謂ｸｲ犧≒ｸ吭ｸｵ犹霞ｸ･犧ｭ犧犧伶ｹ財ｸｲ犹もｸ謂ｸ伶ｸ｢恷犧扉ｸｹ犧吭ｸｰ犧犧｣犧ｱ犧 犹犧ｫ恚犹犧呻恚犧吭ｹ犧｣犧ｷ犹謂ｸｭ犧犧吭ｸｴ犧｢犧ｲ犧｡ 犧犹財ｸｲ犧謂ｹ財ｸｲ犧≒ｸｱ犧扉ｸ犧ｧ犧ｲ犧｡ 犹≒ｸ･犧ｰ犧ｫ犧･犧ｱ犧≒ｸ≒ｸｲ犧｣犧怺犧ｭ犧 犧ｪ怺犧ｧ犧吭ｹ犧伶ｸ犧吭ｸｴ犧犧謂ｸｰ犧怺犧ｭ犧｢ 犹犹犧樅ｸｴ犹謂ｸ｡犧樅ｸｹ犧吭ｸ謂ｸｲ犧≒ｸ≒ｸｲ犧｣犧伶ｹ財ｸｲ犹もｸ謂ｸ伶ｸ｢恷犧吭ｸｰ犧犧｣犧ｱ犧 犧謂ｸｲ犧≒ｸ吭ｸｱ犹霞ｸ吭ｹ犧ｫ恚犹犧呻恚犧吭ｹ犧吭ｹ犧｣犧ｷ犹謂ｸｭ犧犧≒ｸｲ犧｣犹犧もｸｵ犧｢犧吭ｹ≒ｸ憫ｸ吭ｸ犧ｲ犧樅ｹもｸ扉ｸ｢犹犧霞ｸ樅ｸｲ犧ｰ犧樅ｸｧ犧≒ｹもｸ謂ｸ伶ｸ｢恷犧伶ｸｵ犹謂ｸ｡犧ｵ 犹犧奇恚犧ｲ 犹犧｢犹犧, 犧杳ｸ吭ｸ歩ｸ 犹犧｡怺犧歩ｸ 犧もｸｭ犹犧ｫ恚犧ｪ犧吭ｸｸ犧≒ｸ吭ｸｰ犧犧｣犧ｱ犧 犧内ｸｱ犧