Hey so I searched quite a bit for this type of question and i couldn't find any help. - Prove: If B⊂A or A⊂B then P(A∪B) = P(A)∪P(B) and prove the opposite if P(A∪B) = P(A)∪P(B) then B⊂A
so I i think I got the first part correct- A⊂B→ x∈A→ x∈B→ {x}∈P(A)→ {x}∈P(B)→ x∈A∪B→ {x}∈P(A∪B) A⊂B→ x∈A→ x∈B→ {x}∈P(A)→ {x}∈P(B)→ {x}∈P(A)∪P(B) But for the second part it says I should do the negation of the problem but I don't exactly know where to start. Any help would be much appreciated! Also any good courses on set theory would also be appreciated!