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 this properly. It seems like you want to fill in the missing words to explain some fundamental concepts of set theory. Here’s a completion of the provided text:

---

Let $A$ and $B$ be sets.
When $b$ belongs to the set $A$, we write $b \in A$.
When $b$ does not belong to 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 $A$ belongs to the set $B$, and if each element in the set $B$ belongs to the set $A$.
If the set $A$ is not equal to the set $B$, we write $A \neq B$.

---

This describes the concepts of element membership in sets and equality between sets.

Would you like more details or have any questions?

Here are five related questions to think about:

1. What is the meaning of the subset relation $A \subseteq B$?
2. How do we define the union and intersection of two sets?
3. What is the difference between proper subsets and regular subsets?
4. Can a set be a member of itself? Under what conditions is this considered?
5. How can we define set differences and symmetric differences between two sets?

Tip: In set theory, it's important to clearly distinguish between sets and their elements. Set membership and set equality are foundational for more complex operations.