Trabajo de grafos... Tema Leyes de conjuntos

1. Instituto Universitario Politécnico
“Santiago Mariño”
Sede Barcelona
Faculta Ing. De Sistema
Leyes de Conjuntos
Profesor:
Asdrúbal Rodríguez
Integrante:
Parra Rafael
CI:22572054
Barcelona, noviembre 2014

2. LEYES DE CONJUNTOS
 Sean U, A,B,C los siguientes conjuntos
 U={0,1,2,3,4,5,6,7,8}
 A={0,1,2,3}
 B={2,4,5,6,}
 C= {2,5,6,7,8}
Resolver los siguientes conjuntos

3. LEYES DE CONJUNTOS
 Ley de Idempotencia
A ∪ A=A
A ∪ A = {0,1,2,3,} ∪ {0,1,2,3,} = {0,1,2,3,}
A ∪ A=A
B ∩ B= B
{0,1,2,3,} = {0,1,2,3,}
B ∩ B={2,4,5,6} ∩ {2,4,5,6} = {2,4,5,6}
B ∩ B= B
{2,4,5,6} = {2,4,5,6}

4. LEYES DE CONJUNTOS
 Asociativa: (A ∪B) ∪ C = A ∪(B ∪C)
(A ∪B) ∪ C
A ∪B={0,1,2,3,} ∪ {2,4,5,6} ={0,1,2,3,4,5,6}
(A ∪B) ∪ C ={0,1,2,3,4,5,6} ∪ {2,5,6,7,8} ={0,1,2,3,4,5,6,7,8}
{0,1,2,3,4,5,6,7,8}
(A ∪B) ∪ C=
A ∪( B ∪ C)
B ∪ C= {2,4,5,6} ∪ {5,6,7,8} ={2,4,5,6,7,8}
A ∪( B ∪ C) ={0,1,2,3,} ∪ {2,4,5,6,7,8}={0,1,2,3,4,5,6,7,8}
A ∪(B ∪C) =
{0,1,2,3,4,5,6,7,8}
(A ∪B) ∪ C = A ∪(B ∪C)
{0,1,2,3,4,5,6,7,8} = {0,1,2,3,4,5,6,7,8}

5. LEYES DE CONJUNTOS
 Conmutativa: (A∪B) = (B∪A)
(A ∪B)
A∪B={0,1,2,3} ∪ {2,4,5,6}={0,1,2,3,4,5,6}
(A ∪B) =
(B ∪A)
{0,1,2,3,4,5,6}
B∪A={2,4,5,6,} ∪{0,1,2,3}= {0,1,2,3,4,5,6}
(B ∪A)=
{0,1,2,3,4,5,6}
(A∪B) = (B∪A)
{0,1,2,3,4,5,6} = {0,1,2,3,4,5,6}

6. LEYES DE CONJUNTOS
 Conmutativa: (A∩B) = (B∩A)
(A∩B)
A∩B={0,1,2,3} ∪ {2,4,5,6}={2}
(A∩B) =
{2}
(B∩A)
B∩A= {2,4,5,6} ={0,1,2,3} ={2}
{2}
(B∩A) =
(A∩B) = (B∩A)
{2} = {2}

7. LEYES DE CONJUNTOS
 Distributiva: A ∪(B ∩C)=(A ∪B) ∩(A ∪C)
A ∪(B ∩C)
B ∩C={2,4,5,6} ∩{2,5,6,7,8}=2
A ∪(B ∩C)={0,1,2,3} ∪{2}={2}
A ∪(B ∩C)=
{0,1,2,3 }
(A ∪B) ∩(A ∪C)
A ∪B={0,1,2,3} ∪{2,4,5,6}={0,1,2,3,4,5,6}
A ∪C ={0,1,2,3} ∪{2,5,6,7,8}={0,1,2,3,5,6,7,8}
(A ∪B) ∩(A ∪C)={0,1,2,3,4,5,6} ∩ {0,1,2,3,5,6,7,8}={0,1,2,3,5,6}
(A ∪B) ∩(A ∪C)=
{0,1,2,3,5,6 }

8. LEYES DE CONJUNTOS
 De Identidad: A ∪ U=U
A ∪ U={0,1,2,3} ∪{0,1,2,3,4,5,6,7,8}={0,1,2,3,4,5,6,7,8}
A ∪ U=U
{0,1,2,3 ,4,5,6,7,8}
A ∩ U=A
A ∩ U={0,1,2,3} ∩{0,1,2,3,4,5,6,7,8}={0,1,2,3}
A ∩ U=A
{0,1,2,3 }={0,1,2,3}