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# Algebra conjuntoswm

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### Transcript

• 1. ÁLGEBRA DE CONJUNTOS
Wendy Lorena Motivar Cepeda
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
A
B
A U B= B U A
• 7. 1,2,3,4,5
1,2,3,4,5
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