Let’s solve this problem!

Problem:

We are given the set $B = \{3, 6, 9\}$ and asked to find the intersection $B \cap \emptyset$, where $\emptyset$ denotes the empty set.

Solution:

The intersection of two sets $A$ and $B$ is defined as the set of all elements that belong to both $A$ and $B$. Symbolically: $A \cap B = \{ x \mid x \in A \text{ and } x \in B \}.$

Since $\emptyset$ contains no elements, there cannot be any common elements between $B$ and $\emptyset$. Therefore: $B \cap \emptyset = \emptyset.$

Answer:

The correct option is:

• B. The set $B \cap \emptyset$ is the empty set.

Let me know if you'd like more explanation! 😊

Related Questions:

1. What is the definition of the empty set and its properties?
2. How does set intersection differ from set union?
3. If $B = \{3, 6, 9\}$ and $C = \{6, 9, 12\}$, what is $B \cap C$?
4. What happens when you take the union $B \cup \emptyset$?
5. How does the intersection operation behave with disjoint sets?

Tip:

Remember, the empty set $\emptyset$ acts like a "zero" in set intersection because it has no elements to contribute!