Leyes de Conjunto

1. LEYES DE
CONJUNTOS
Juan G Marcano F
CI: 15.376.313
E.D. y Grafos

2. LEY DE IDEMPOTENCIA
AUA= A
A= {a,b,c,d}
AUA= {a,b,c,d}
LEY ASOCIATIVA
(AUB) UC = AU(BUC)
A= {2,4,5,6}
B= {1,3,4,7}
C= {2,3,8,9}
(AUB)= {1,2,3,4,5,6,7}
(AUB) UC= {1,2,3,4,5,6,7,8,9}
(BUC)= {1,2,3,4,7,8,9}
AU(BUC)= {1,2,3,4,5,6,7,8,9}
(AUB) UC = AU(BUC)
{1,2,3,4,5,6,7,8,9} = {1,2,3,4,5,6,7,8,9}

3. LEY CONMUTATIVA
AUB=BUA
A={2,4,5,6}
B={1,3,4,7}
AUB={1,2,3,4,5,6,7}
BUA={1,2,3,4,5,6,7}
AUB = BUA
{1,2,3,4,5,6,7} = {1,2,3,4,5,6,7}
LEY DISTRIBUTIVA
AU(B∩C)= (AUB) ∩(AUC)
A={2,4,5,6}
B= {1,3,4,7}
C= {2,3,8,9}
B∩C={3}
AU(B∩C)= {2,3,4,5,6}
AUB= {1,2,3,4,5,6,7}
AUC= {2,3,4,5,6,8,9}
(AUB) ∩(AUC)= {2,3,4,5,6}
AU(B∩C) = (AUB) ∩(AUC)
{2,3,4,5,6} = {2,3,4,5,6}

4. LEY DE MORGAN
E={1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,9}
B= {2,4,6,10}
(AUB)´ =A´∩ B´
AUB= {1,2,3,4,5,6,7,9,10}
(AUB)´= {7,8}
A´= {2,4,6,7,8,10}
B´= {1,3,5,7,8,9}
A´∩ B´= {7,8}
(AUB)´ =A´∩ B´
{7,8} = {7,8}