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Algebra conjuntoswm
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Algebra conjuntoswm

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  • 1. ÁLGEBRA DE CONJUNTOS
    Wendy Lorena Motivar Cepeda
  • 2. Dados los conjuntos:
    A ={1,2,3,4,5}
    B={6,7,8,9,0}
    C={2,4,6,8}
    D={3,5,7,9}
    E={6,7,8}
    F={Ø}
  • 3. Desarrollar:
    A
    A ∩ A = A
    A
    A U A = A
  • 4. A
    F
    A ∩ Ø =Ø
    Ø
    Elemento neutro de la Unión
    A
    A U Ø =A
    F
  • 5. 1,2,3,4,5
    1,2,3,4,5
    Elemento neutro de la Intersección
    U
    A
    A ∩ U=A
    U
    A UU=U
    A
  • 6. Propiedad conmutativa de la intersección
    A
    B
    A ∩ B= B ∩ A
    Propiedad conmutativa de la unión
    A
    B
    A U B= B U A
  • 7. 1,2,3,4,5
    1,2,3,4,5
    Propiedad de involución
    U
    AC =
    A
    U
    (AC)C = A
    A
  • 8. Propiedad asociativa de la intersección
    (A ∩ B) ∩ C= A ∩(B ∩ C) -> Ø
    A
    B
    2 4
    6 8
    C
  • 9. Propiedad asociativa de la intersección
    (A U B) U C= A U(B U C)
    A
    B
    2 4
    6 8
    C
  • 10. Propiedad distributiva de la intersección
    A ∩(B U C) = (A ∩ B) U (A ∩ C)
    A
    B
    A
    B
    1 3 5
    7 9 0
    1 3 5
    7 9 0
    6 8
    2 4
    2 4
    6 8
    C
    C
    (A ∩ B)
    (B U C)
    (A ∩ C)
    A ∩(B U C)
    (A ∩ B) U (A ∩ C)
  • 11. ACU BC = (A ∩ B) C
    U
    A
    B
    2 4
    6 8
    C
    AC
    (A ∩ B) C
    BC
  • 12. AC∩ BC = (A U B) C -> Ø
    U
    A
    B
    2 4
    6 8
    C
  • 13. Propiedad distributiva de la unión
    A U (B ∩ C) = (A U B) ∩ (A U C)
    A
    B
    A
    B
    1 3 5
    7 9 0
    1 3 5
    7 9 0
    6 8
    2 4
    6 8
    2 4
    C
    C
    (B ∩ C)
    (A U B)
    (A U C)
    A U (B ∩ C)
    (A U B) ∩ (A U C)
  • 14. A ∩ B C AC A U B
    A
    B
  • 15. C (A ∩ B) = (C A) U (C B)
    A
    B
    A
    B
    1 3 5
    1 3 5
    7 9 0
    7 9 0
    6 8
    2 4
    6 8
    2 4
    C
    C
    (A ∩ B)
    (C A)
    (C B)
    C (A ∩ B)
    (C A) U (C B)
  • 16. C (A U B) = (C A)∩ (C B)
    A
    B
    A
    B
    1 3 5
    1 3 5
    7 9 0
    7 9 0
    6 8
    2 4
    6 8
    2 4
    C
    C
    (A U B)
    (C A)
    (C B)
    C (A U B)
    (C A)∩(C B)
  • 17. C (B A) = (A ∩ C)U (C B)
    A
    B
    A
    B
    1 3 5
    1 3 5
    7 9 0
    7 9 0
    6 8
    2 4
    6 8
    2 4
    C
    C
    (B A)
    (A ∩ C)
    (C B)
    C (B A)
    (A ∩ C) U (C B)
  • 18. (B A) ∩ C = (B ∩ C) AU = B ∩ (C A)
    A
    B
    A
    A
    1 3
    5
    1 3
    5
    1 3
    5
    B
    B
    7 9
    0
    7 9
    0
    7 9
    0
    2 4
    2 4
    2 4
    6 8
    6 8
    6 8
    C
    C
    C
    (B A)
    (B ∩ C)
    (C A)
    (B A) ∩ C
    B ∩ (C A)
    (B ∩ C) A
  • 19. (B A) UC = (B UC) (A C)
    A
    B
    A
    B
    1 3 5
    1 3 5
    7 9 0
    7 9 0
    6 8
    2 4
    6 8
    2 4
    C
    C
    (B A)
    (B U C)
    (A C)
    (B A) U C
    (B U C) (A C)
  • 20. Ø A = Ø
    A Ø = A
    A A = Ø
    A
    A
    F
    A
    F
  • 21. A B = A ∩ BC
    U
    A
    B
    A
    B
    A B
    BC
    A ∩ BC
  • 22. (B A)C = A U BC
    U
    U
    A
    B
    A
    B
    B A
    BC
    (B A)C
    A U BC
  • 23. 1,2,3,4,5
    1,2,3,4,5
    U
    A
    U A = AC
    U
    A
    A U = Ø

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