Complete the following: Let A and B be sets. When b the set A we write b ∈ A . When b the set A we write b ∉ A . We say the set A the set B and write A

Let's complete the given statements in a mathematically sound way:

Let $A$ and $B$ be sets.

• When $b$ is an element of the set $A$, we write $b \in A$.
• When $b$ is not an element of the set $A$, we write $b \notin A$.
• We say the set $A$ is equal to the set $B$ and write $A = B$ if each element in the set $A$ is in the set $B$, and if each element in the set $B$ is in the set $A$.
• If the set $A$ is not equal to the set $B$, we write $A \neq B$.

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Here are 5 related questions:

1. What is the definition of a subset in set theory?
2. How do you define the union of two sets?
3. What is the intersection of two sets, and how is it written?
4. How can we show that two sets are equal using the subset method?
5. What does the difference between two sets $A - B$ represent?

Tip: In set theory, showing equality of two sets often involves proving both $A \subseteq B$ and $B \subseteq A$.