The given statement in the image is:

If $A \subseteq B$, then $(B - A) \cap A = \emptyset$.

Explanation:

• $A \subseteq B$ means that $A$ is a subset of $B$, i.e., every element of $A$ is also an element of $B$.
• $B - A$ represents the set of elements that are in $B$ but not in $A$.
• The intersection $(B - A) \cap A$ asks for common elements between $A$ and $B - A$.

Analysis:

If $A \subseteq B$:

• The set $A$ contains elements exclusively from $B$.
• The set $B - A$ contains elements in $B$ but excludes all elements of $A$.
• Since $A$ and $B - A$ have no overlapping elements (by definition), their intersection is the empty set $\emptyset$.

Thus, the statement $(B - A) \cap A = \emptyset$ is correct.

Let me know if you have any questions or want more details on this!

Here are 5 related questions for exploration:

1. How does this principle extend to disjoint sets?
2. What happens if $A = B$ in this situation?
3. How can the complement of $A$ in $B$ be visualized using a Venn diagram?
4. Can you prove this statement using a formal set-theoretic proof?
5. What are some practical applications of this property in real-world scenarios?

Tip: A quick way to verify such relations is by visualizing the sets with a Venn diagram!