Ejercicios de conjuntos

1. Universidad Central del Ecuador
Facultad de Filosofía, Letras y Ciencias de la Educación
Carrera de Pedagogía de las Ciencias Experimentales,
Química y Biología
Curso: Primero "B"
Materia: Matemática
Docente: Dr. Manuel Humberto Chiriboga
Quishpe Karen
Integrantes:
Tema: Taller #1

2. DATOS:
Dados los conjuntos:
A= {0, 2, 4, 6, 8, 10, 12}
B = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C = {0, 1, 3, 5, 7, 9, 11}
Resuelva los siguientes ejercicios:

3. A
Ley de idempotencia
A U A = A
U
A U A= {0, 2, 4, 6, 8, 10, 12}

4. A ∩A = A
A
U
A ∩A= {0, 2, 4, 6, 8, 10, 12}

5. B
Leyes conmutativas
A U B = B U A
A
U
A U B = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}
B U A = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}

6. A ∩B = B ∩A
B
A
U
A ∩B= {0, 2, 4, 6, 8, 10}
B ∩A= {0, 2, 4, 6, 8, 10}

7. LEYES ASOCIATIVAS
A U (B U C) = (A U B) U C
c
A
B
U
B U C = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A U (B U C) = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A U B = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}
(A U B) U C = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

8. (A ∩B) ∩C = A ∩(B ∩C)
c
A
B
U
A ∩B = {0, 2, 4, 6, 8, 10}
(A ∩B) ∩C = {0, 2, 4, 6, 8, 10}
B ∩C = { 0 }
A ∩(B ∩C) = {0, 2, 4, 6, 8, 10}

9. LEYES DISTRIBUTIVAS
A U (C ∩B) = (A U C) ∩ (A U B)
c
A
B
U
A U C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
C ∩B = { 0, 1, 3, 5, 7, 9 }
A U (C ∩B) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}
A U B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}
(A U C) ∩(A U B) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,12}

10. A ∩(C U B) = (A ∩C) U (A ∩B)
c
A
B
U
C U B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ∩(C U B) = {0, 1, 3, 5, 9}
A ∩C = {0}
A ∩B = {0, 2, 4, 6, 8, 10}
(A ∩C) U (A ∩B) = {0, 2, 4, 6, 8, 10}

11. LEYES DE IDENTIDAD
A U ∅= A
A
U
A U ∅= {0, 2, 4, 6, 8, 10, 12}

12. A
U
A U U = U
A U U= {0, 2, 4, 6, 8, 10, 12}

13. U
A ∩∅= ∅
A ∅
A ∩∅= {∅}

14. A
A ∩U = A
A ∩U = {0, 2, 4, 6, 8, 10, 12}
U

15. U
LEYES DE COMPLEMENTO
A U A' = U
A
A'
A U A' = { U }

16. A
U
A ∩A' = ∅
A = {0, 2, 4, 6, 8, 10, 12}
A' = U = {∅}
A ∩A'= {∅}

17. U
(A')' = A
A
(A')' = {0, 2, 4, 6, 8, 10, 12}

18. U
U' = ∅
U' = {∅}

19. U
∅' = U
∅' = { U }

20. A
B
U
A ∩B' = A - B
A= {0, 2, 4, 6, 8, 10, 12}
B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12}
B' = {0, 2, 4, 6, 8, 10, 12}
A - B = {12}

21. LEYS DE MORGAN
(A U B)' = A' ∩B'
A B
U
(A U B)' = {∅}
A U B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12}
A' ∩B'= {∅}

22. B
U
(A ∩B)' = A' U B'
A
A ∩B = {0, 2, 4, 6, 8, 10}
(A ∩B)' = {1, 3, 5, 7, 9}
A' = {1, 3, 5, 7, 9}
B' = {12}
A' U B' = {U}