LAS 5 LEYES DE CONJUNTOSEjercicios

Por Miguel Carrera C.I 25.687.509

Barcelona 19 de noviembre del 2014

Conjuntos a utilizar:M={A,B,C}A={2,4,6,8,10,12,16,18,20}B={3,6,9,12,15,18}C={4,8,12,16,20}

DE IDEMPOTENCIA A ∪ A = A A ∩ A = A

AuA=(2,4,6,8,10,12,16,18,20)u(2,4,6,8,10,12,16,18,20)

Resultado:A=(2,4,6,8,10,12,16,18,20)

B∩B=(3,6,9,12,15,18) ∩(3,6,9,12,15,18)

Resultado B=(3,6,9,12,15,18)

Asociativa:(AuB) u C =A u (BuC)(AuB) u C

AuB={2,4,6,8,10,12,16,18,20}u{3,6,9,12,15,18}={2,3,4,6,8,9,10,12,15,16,18,20}

(AuB)u C={2,3,4,6,8,9,10,12,15,16,18,20}U{4,8,12,16,20}={2,3,4,6,8,9,12,15,16,18,20}

Resultado ={2,3,4,6,8,9,12,15,16,18,20}

A u (BuC)BuC={3,6,9,12,15,18} U{4,8,12,16,20}={3,4,6,8,9,12,15,16,15,20}

Au(BuC)={2,4,6,8,10,12,16,18,20}u{3,4,6,8,9,12,15,16,15,20}={2,4,6,8,9,10,12,15,16,18,20}

Resultado ={2,3,4,6,8,9,12,15,16,18,20}

AuB={2,4,6,8,10,12,16,18,20}u{3,6,9,12,15,18}={2,3,4,6,8,9,10,12,15,16,18,20}

BuA={3,6,9,12,15,18}u{2,4,6,8,10,12,16,18,20}={2,3,4,6,8,9,10,12,15,16,18,20}

Conmutativa:(AuB)=(BuA)

Distributiva: A u (B ∩ C) =(AuB) ∩ (Auc)

Au(B ∩ C) B∩C={3,6,9,12,15,18} ∩{4,8,12,16,20}={12}Au(B ∩C)={2,4,6,8,10,12,16,18,20}U{12} ={2,4,6,8,10,12,16,18,20}

Resultado={2,4,6,8,10,12,16,18,20}

(AuB) ∩ (AuC)AuB={2,4,6,8,10,12,16,18,20}u{3,6,9,12,15,18}={2,3,4,6,8,9,10,12,15,16,18,20}

AuC={2,4,6,8,10,12,16,18,20}u{4,8,12,16,20}={2,4,6,8,10,12,16,18,20}

AuB ∩(AuC) ={2,4,6,8,10,12,16,18,20}

A∩B={2,4,6,8,10,12,16,18,20}u{3,6,9,12,15,18}={2,4,6,8,10,12,16,18,20}

AUB={2,4,6,8,10,12,16,18,20}U {3,6,9,12,15,18} ={3,6,9,12,15,18}

A ∩ ∅ = ∅

DE IDENTIDAD A ∪ U = U A ∩ U = A