Questions to complete during the tutorial

of essential material Set theory For your reference we collect some facts on set theory. We always look at a base setX and subsets thereof. Here are some precise definition: • A ⊆ X is a subset of X if x ∈ A implies x ∈ X. The collection of all subsets of X is called the power set of X. We denote the power set of X by (X). • If A,B ⊆ X we write A ⊆ B if x ∈ B for every x ∈ A and A = B if A ⊆ B and B ⊆ A. • Let I be an arbitrary index set, for instance I = {1, 2,... , n} finite, I = N countable or I = R uncountable. There is no restriction on the cardinality of I . Suppose that for every i ∈ I there is a set Ai ⊆ X. We define the union