1) The document defines four sets: U={0,1,2,3,4,5,6,7,8}, A={0,1,2,3}, B={2,4,5,6}, and C={2,5,6,7,8}. 2) It then solves examples demonstrating set laws, such as idempotence, associativity, commutativity, distributivity, and identity. 3) For each law, it provides the mathematical operations and resulting sets to show the law holds true for the given sets A, B, C and U.

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}