Universal set X, Let {A_1,A_2,A_3,…}
{A_1,A_2,A_3,…}={ A_n }_(n=1)^∞ʕ P(x) can be a sequence of sets S

Define B_i:=A_(i )
n≥2 B_n≔ A_n∩A_(n-1)^C∩…∩A_n^c
Prove that {B_n }_(n=1)^∞ is pairwise disjoint
Show B_i∩B_j=0 whenever 1≠j
Prove ∪_(k=1)^n A_k=∪_(k=1)^n B_k for every positive integer.

Question

Universal set X, Let {A_1,A_2,A_3,…}
{A_1,A_2,A_3,…}={ A_n }_(n=1)^∞ʕ P(x) can be a sequence of sets S 

Define B_i:=A_(i   )
n≥2 B_n≔ A_n∩A_(n-1)^C∩…∩A_n^c
Prove that {B_n }_(n=1)^∞ is pairwise disjoint
Show B_i∩B_j=0 whenever 1≠j
Prove ∪_(k=1)^n A_k=∪_(k=1)^n B_k for every positive integer.

anonymous · Answer

that weird little backwards question marky thig was supposed to be subset. but it doent look right on here.