第五章-集合论-ä&s

第五章-集合论-ä&s

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Unformatted text preview: 12 èa 2 22 {-32 2} 2 42 {52 62 72 82 92 102 112 122 132 142 15} 22 èa 2 22 {x| x 2 2 42 {x|® x ø¶ª* 8 10< x< 20} } 2 62 {x| x=2k+12 k∈I} * 4.× èÈFÿµª*4 ª1 ¶ 2 5. PûÖ 2 èa 6èa 2 22 ρ {12 ∅}2 ={∅ {1}2 {∅}2 {12 ∅}} 2 4 2 ρ {∅ {a} 2 {∅}} 2 ={∅ {∅} 2 {{a}} 2 {{∅}} 2 {∅ {a}} 2 {∅ {∅}}2 {{a}2 {∅}}2 {∅ {a}2 {∅}}} 102 2 2 82 ρ A2 − C2 ρ 2 ρ A2 − C2 ρ ={∅ {1}2 {4}2 {12 4}}− ∅ {2}2 {4}2 {22 4}} { U={12 22 32 42 5}2 A={12 4}2 B={12 22 5}2 C={22 4}2 62 {{12 2}2 {22 12 1}2 {22 12 12 2}}={{12 2}} ∅ {{12 2}} A=G2 B=E2 C=F I2 ={{1}2 {12 4}} ª 11X* 9F · 2 12 A− B∩ C2 =2 A− 2 2 2 A− 2 B C 2 32 A∩ B∪ C2 =2 A∩ B2 2 2 A∩ C2 2 42 A∩ A − 2 = A−B B 2 12 A− B∩C2 = A∩ ∼ B∩ C2 = A∩ ∼ B∪ ∼ C2 =2 A∩ ∼ B2 ∪ A∩ ∼ C2 =2 A− 2 ∪ A− 2 B C 2 ª 3XΦ ·9 x x∈ A∩ B∪ C2 x ⇔ x∈ A∧ ∈ B∪ C x ⇔ x∈ A∧ x∈ B∨ ∈ C2 x x ⇔ x∈A∧ ∈ B2 ∨ x∈A∧ ∈ C2 ⇔x∈ A∩ B2 ∨x∈ A∩C2 ⇔x∈ A∩ B2 ∪ A∩C2 2 42 A∩ A −B2 = A∩ A ∩ ∼ B = A ∩∼B =A − B 122 A2 B2ª ¶ C è*ÈFÿµª4 × 1 12 2 32 A− 2 ∪ A− 2 =A B C A− 2 ∩ A− 2 = ∅ B C 12 A− 2 ∪ A− 2 B C = 2 A∩ ∼ B2 ∪ A∩ ∼ C2 = A∩ ∼ B∪ ∼ C2 = A∩ ∼ B∩ C2 = A− B∩ C2 2 2 32 A− 2 ∪ A− 2 =A 2 B C A∩ B∩C2 =∅ A− 2 ∩ A− 2 B C 2 − A− B∩ C2 =A = 2 A∩ ∼ B2 ∩ A∩ ∼ C2 = A∩ ∼ B∩ ∼ C2 = A∩ ∼ B∪ C2 = A− B∪ C2 2 A− 2 ∩ A− 2 =∅ 2 B C A⊆ B∪CØ 13. 2 A2 B 2 2 12 2 A− B=B2 12 A=B=φ A− B=B B B ⇔ 2 A− ⊆ B2 ∧ B⊆ A− 2 B) B B) ⇔ ( A− ∩ B= A− 2 ∧ B∩ ( A− = B2 A 2· 9B Hª G * A− B∪C2 =∅ 5.112 B ⇔ 2 A ∩ ~ B ∩ B= A− 2 ∧ B ∩A ∩ ~ B = B2 B= ⇔ 2 A− φ ∧ B=φ ⇔ A ⊆ B∧B=φ ⇔ A=B=φ A− B=B B B B ⇔ A− ⊆ B∧ ⊆ A− B B= B ⇔A− − φ∧ B− A− 2 =φ B= ⇔ A− φ∧ B∩~A2 ∪ B∩ B2 =φ B= A= ⇔ A− φ∧ B− φ∧ B=φ B ⇔ A ⊆ B∧ ⊆ A∧B=φ ⇔ A=B=φ 15. 2 A={{φ }2 {{φ }}}2 2 42 ∪ ρ A2 2 ∪ ρ A2 =∪ {φ {{φ }}2 {{{φ }}}2 {{φ }2 {{φ }}} ={{φ }2 {{φ }}} =A 16. 2 B={{12 2}2 {22 3}2 {12 3}ª2¶ φ 8}x *® 2 32 ∩ ∪B2 2 24.2 32 ∩ ∪B2 =∩{12 22 3}=1∩ 2∩3 A={02 1}2 B={1ª 2 ®2}x *¶8 22 A× B 2 22 A× B={<0,1>,<0,2>,<1,1>,<1,2>} 26.2 A2 ¬ BÐ 28C ¸ E é* ª · J 2 22 A× 2 ª 92¸ ·@ B∪ C2 =2 A× B2 ∪ A× C2 x, y y x, y ∈ A × ( B U C ) ⇔ x ∈ A ∧ y ∈ B UC ⇔ x ∈ A ∧ ( y ∈ B ∨ y ∈C ) ⇔ ( x ∈ A ∧ y ∈ B) ∨ ( x ∈ A ∧ y ∈C ) ⇔ ( x, y ∈ A × B ) ∨ ( x, y ∈ A × C ) ⇔ x, y ∈ ( A × B ) U ( A × C ) ∈ 27. ·@ *¸ ª A× ( B UC ) = ( A × B ) U( A × C ) A ⊆ C B ⊆D x,y A×B⊆ C×D x,y ∈ A×B y ⇔x∈A∧ ∈B ⇒ x∈C ∧y∈D 8H ⇔ x,y ∈ C×D (Ð A× B ⊆ C×D ∈A ⊆ C B ⊆ D ) ...
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This note was uploaded on 02/06/2011 for the course CS 343 taught by Professor Zhoujunli during the Spring '08 term at BUPT.

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