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
=
B
if each element in the set
A
the set
B
and if each element in the set
B
the set
A
.
If the set
A
the set
B
we write
A
≠
B
.

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.

Let A and B be sets. When b belongs to the set A we write b ∈ A. When b does not belong to the set A we write b ∉ 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 ≠ B.

Learn the basics of set theory, including the concepts of set membership, set equality, and element belonging. This guide provides detailed explanations and examples suitable for students in Grades 9-12.

Math Problem Statement

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

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