resolución de 5 leyes conjuntos iupsm
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I.U.P.S.M.LEYES DE CONJUNTOS
LEYES DE CONJUNTOSLEYES DE CONJUNTOS
República Bolivariana de VenezuelaMinisterio 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
I.U.P.S.M.LEYES DE CONJUNTOS
CONTENIDO
De idempotencia
Asociativa
Conmutativa
Distributiva
De Identidad
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.
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
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} =
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}
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}
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}
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}
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}
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
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}
I.U.P.S.M.LEYES DE CONJUNTOS