This document discusses set theory laws and provides examples to demonstrate idempotence, associativity, commutativity, distributivity, and identity laws using the sets U={11,22,33,44,55,66,77,88,99}, A={11,22,33,44}, B={44,55,66,77}, and C={11,44,88,99}. It shows that the union and intersection of a set with itself is equal to the set, that order does not matter in unions and intersections, that unions and intersections can be distributed over each other, and that the union of a set with the universal set U and the intersection of a set with the empty set
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Resolución de 5 Leyes conjuntos IUPSM
1. I.U.P.S.M.LEYES DE CONJUNTOS
LEYES DE CONJUNTOS
República Bolivariana de Venezuela
Ministerio del Poder Popular para la Educación
INSTITUTO UNIVERSITARIO POLITÉCNICO “SANTIAGO MARIÑO”
Cátedra: Estructuras Discretas y Grafos
Profesor:
Ing. Asdrúbal Rodríguez
Junio, 2014
Participante:
Carrasquel, Jean Carlos
Sección: SV
3. I.U.P.S.M.LEYES DE CONJUNTOS
Sean U, A, B, C los siguientes conjuntos:
U = {11, 22, 33, 44, 55, 66, 77, 88, 99}
A = {11, 22, 33, 44}
B = {44, 55, 66, 77}
C = {11, 44, 88, 99}
Utilizados para resolver las principales Leyes de Conjuntos.
4. I.U.P.S.M.LEYES DE CONJUNTOS
De idempotencia:
A A = A
A A = {11, 22, 33, 44} {11, 22, 33, 44} = {11, 22, 33, 44}
B B = B
B B = {44, 55, 66, 77} {44, 55, 66, 77} = {44, 55, 66, 77}
{11, 22, 33, 44} = {11, 22, 33, 44}
A A = A
{44, 55, 66, 77} = {44, 55, 66, 77}
B B = B
5. I.U.P.S.M.LEYES DE CONJUNTOS
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {11, 22, 33, 44, 55, 66, 77}
Asociativa:
(A B) C
(A B) C = {11, 22, 33, 44, 55, 66, 77} {11, 44, 88, 99} = {11, 22, 33, 44, 55, 66, 77, 88, 99}
{11, 22, 33, 44, 55, 66, 77, 88, 99}(A B) C =
B C = {44, 55, 66, 77} {11, 44, 88, 99} = {11, 44, 55, 66, 77, 88, 99}
A (B C)
A (B C) = {11, 22, 33, 44} {11, 44, 55, 66, 77, 88, 99} = {11, 22, 33, 44, 55, 66, 77, 88, 99}
{11, 22, 33, 44, 55, 66, 77, 88, 99}A (B C) =
(A B) C = A (B C)
(A B) C = A (B C)
{11, 22, 33, 44, 55, 66, 77, 88, 99} {11, 22, 33, 44, 55, 66, 77, 88, 99}=
6. I.U.P.S.M.LEYES DE CONJUNTOS
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {44}
Asociativa:
(A B) C
(A B) C = {44} {11, 44, 88, 99} = {44}
{44}(A B) C =
B C = {44, 55, 66, 77} {11, 44, 88, 99} = {44}
A (B C)
A (B C) = {11, 22, 33, 44} {44} = {44}
{44}A (B C) =
(A B) C = A (B C)
{44} =
(A B) C = A (B C)
{44}
7. I.U.P.S.M.LEYES DE CONJUNTOS
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {11, 22, 33, 44, 55, 66, 77}
Conmutativa:
(A B)
{11, 22, 33, 44, 55, 66, 77}(A B) =
B A = {44, 55, 66, 77} {11, 22, 33, 44} = {11, 22, 33, 44, 55, 66, 77}
(B A)
{11, 22, 33, 44, 55, 66, 77}(B A) =
(A B) = (B A)
=
(A B) = (B A)
{11, 22, 33, 44, 55, 66, 77} {11, 22, 33, 44, 55, 66, 77}
8. I.U.P.S.M.LEYES DE CONJUNTOS
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {44}
Conmutativa:
(A B)
{44}(A B) =
B A = {44, 55, 66, 77} {11, 22, 33, 44} = {44}
(B A)
{44}(B A) =
(A B) = (B A)
=
(A B) = (B A)
{44} {44}
9. I.U.P.S.M.LEYES DE CONJUNTOS
B C = {44, 55, 66, 77} {11, 44, 88, 99} = {44}
Distributiva:
{11, 22 ,33 ,44}A (B C) =
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {11, 22, 33, 44, 55, 66, 77}
A (B C) = (A B) (A C)
=
A (B C)
A (B C) = {11, 22, 33, 44} {44} = {11, 22 ,33 ,44}
(A B) (A C)
A C = {11, 22, 33, 44} {11, 44, 88, 99} = {11, 22, 33, 44, 88, 99}
(A B) (A C) = {11, 22, 33, 44, 55, 66, 77} {11, 22, 33, 44, 88, 99} = {11, 22, 33, 44}
(A B) (A C) = {11, 22 ,33 ,44}
A (B C) = (A B) (A C)
{11, 22 ,33 ,44} {11, 22 ,33 ,44}
10. I.U.P.S.M.LEYES DE CONJUNTOS
B C = {44, 55, 66, 77} {11, 44, 88, 99} = {11, 44, 55, 66, 77, 88, 99}
Distributiva:
{11, 44}
A B = {11, 22, 33, 44} {44, 55, 66, 77} = {44}
A (B C) = (A B) (A C)
=
A (B C)
A (B C) = {11, 22, 33, 44} {11, 44, 55, 66, 77, 88, 99} = {11, 44}
A C = {11, 22, 33, 44} {11, 44, 88, 99} = {11, 44}
(A B ) (A C ) = {44} {11, 44} = {11, 44}
{11, 44}
A (B C) =
(A B) (A C)
(A B) (A C) =
A (B C) = (A B) (A C)
{11, 44} {11, 44}
11. I.U.P.S.M.LEYES DE CONJUNTOS
=
De Identidad:
A U = U
A U = {11, 22, 33, 44} {11, 22, 33, 44, 55, 66, 77, 88, 99} = {11, 22, 33, 44, 55, 66, 77, 88, 99}
A U = U
{11, 22, 33, 44, 55, 66, 77, 88, 99} {11, 22, 33, 44, 55, 66, 77, 88, 99}
=
A U = A
A U = {11, 22, 33, 44} {11, 22, 33, 44, 55, 66, 77, 88, 99} = {11, 22, 33, 44}
{11, 22, 33, 44} {11, 22, 33, 44}
A U = A
12. I.U.P.S.M.LEYES DE CONJUNTOS
=
De Identidad:
A = A
A = {11, 22, 33, 44} { } = {11, 22, 33, 44}
=
A =
A = {11, 22, 33, 44} { } =
{} {}
A =
A = A
{11, 22, 33, 44} {11, 22, 33, 44}