LEYES DE CONJUNTOS

Juan G Marcano FCI: 15.376.313E.D. y Grafos

LEY DE IDEMPOTENCIA

AUA= AA= {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}

LEY CONMUTATIVA

AUB=BUAA={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}

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}