Answer:
Step-by-step explanation:
Consider the sets A and B
(A − (A ∩ B)) ∩ (B − (A ∩ B))
= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) by the set difference law
= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) by De Morgan's law
= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} by the distributive law
= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} by complementation
= {A ∩ Bc} ∩ {B ∩ Ac} by identity law
= (A ∩ Ac) ∩ (B ∩ Ac) by the associative law
= ∅ ∩ ∅ by complementation
= ∅ by the universal bound law
Therefore, (A − (A ∩ B)) ∩ (B − (A ∩ B)) = ∅
Answer:
Considere los conjuntos A y B
(A − (A ∩ B)) ∩ (B − (A ∩ B))
= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) por la ley de diferencia establecida
= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) por la ley de De Morgan
= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} por la ley distributiva
= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} complementando
= {A ∩ Bc} ∩ {B ∩ Ac} por ley de identidad
= (A ∩ Ac) ∩ (B ∩ Ac) por la ley asociativa
= ∅ ∩ ∅ complementando
= ∅ por la ley universal consolidada
Step-by-step explanation:
