The questions are asking you to show equality between different sets. The most common way to do these type of questions is to show that both sets are contained in each other (because A = B iff A ⊇ B and A ⊆ B).

Take question i). You need to show that for any subset X ⊆ E,

X ∈ ¬(Q_1 ∧ Q_2) iff X ∈ ¬Q_1 ∨ ¬Q_2