John-Michael Kuczynski5 days ago1 min read How do you prove that (A ∪ B) ∩ (B ∪ C) ⊆ (A ∪ C)? You don’t, because it’s false.(A ∪ B) ∩ (B ∪ C)=B∪(A∩C)Suppose that [A]=2 and [C]=3 and [B]=75In that case [A ∪ B] ≤5, but B∪(A∩C)= (A ∪ B) ∩ (B ∪ C) ≥ 75, in which case(A ∪ B) ∩ (B ∪ C)> (A ∪ C)0 views0 comments

You don’t, because it’s false.(A ∪ B) ∩ (B ∪ C)=B∪(A∩C)Suppose that [A]=2 and [C]=3 and [B]=75In that case [A ∪ B] ≤5, but B∪(A∩C)= (A ∪ B) ∩ (B ∪ C) ≥ 75, in which case(A ∪ B) ∩ (B ∪ C)> (A ∪ C)