The problem in the image is about set operations. Here’s a breakdown of the information given:

1. Sets are defined as follows:

   • $A \cap B = \{1, 2\}$
   • $B \setminus A = \{4, 5\}$
   • $A \cup B = \{0, 1, 2, 3, 4, 5\}$

2. The task is to find the elements of sets $A$ and $B$ separately.

Solution:

1. Interpret $A \cap B$: This is the intersection of sets $A$ and $B$, meaning these elements are in both $A$ and $B$. So, $A$ and $B$ both contain the elements $\{1, 2\}$.

2. Interpret $B \setminus A$: This represents the elements that are in $B$ but not in $A$. Therefore, $B$ contains the elements $\{4, 5\}$, which are not in $A$.

3. Interpret $A \cup B$: This is the union of sets $A$ and $B$, indicating all elements that are in $A$, in $B$, or in both. The union of $A$ and $B$ is $\{0, 1, 2, 3, 4, 5\}$.

Determine $A$ and $B$:

From the above information, we can deduce the contents of $A$ and $B$:

• Since $A \cup B = \{0, 1, 2, 3, 4, 5\}$, and we know that $B \setminus A = \{4, 5\}$, we conclude:
  • $A$ contains some or all elements from $\{0, 3\}$ along with $\{1, 2\}$ (from the intersection).
  • $B$ contains $\{1, 2, 4, 5\}$ and potentially more from $A \cup B$.

Conclusion:

Based on the union, intersection, and difference, you can determine specific sets for $A$ and $B$.

Would you like further details or a step-by-step breakdown of this solution? Here are some related questions for further practice:

1. How would you find $A \cup (B \setminus A)$?
2. What is the complement of $A \cap B$ in $A \cup B$?
3. Can you determine the symmetric difference $A \Delta B$ with the given data?
4. If $A \subset C$, where $C$ is a superset, what could be $C$'s possible elements?
5. How would the solution change if $B \setminus A$ contained only one element?

Tip: Remember that the union, intersection, and difference of sets are foundational operations for determining relationships between sets.