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Any idea how to do this? Strictly speaking it's a Semantic. problem, but it's math.

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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
by

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