The image asks for the interpretation of set operations using Venn diagrams for three sets $X$, $Y$, and $Z$. The two set expressions to evaluate are:

1. $(X \cap Y) \times Z$
2. $(X \cup Y) \times (Z - Y)$

Here’s a breakdown of each:

1. $(X \cap Y) \times Z$:

   • $X \cap Y$ represents the intersection of sets $X$ and $Y$, which is the portion that belongs to both sets $X$ and $Y$.
   • When intersected with $Z$, you are looking for the part that belongs to both $(X \cap Y)$ and $Z$.

2. $(X \cup Y) \times (Z - Y)$:

   • $X \cup Y$ represents the union of $X$ and $Y$, i.e., all elements that belong to either set $X$ or set $Y$.
   • $Z - Y$ represents the difference, i.e., elements in $Z$ but not in $Y$.
   • The final result is the intersection of the union of $X$ and $Y$ with the set $Z$ excluding $Y$.

Would you like a detailed step-by-step explanation of these operations? Here are some related questions to explore the concepts further:

1. What is the difference between union and intersection in set theory?
2. How do you visualize set operations on a Venn diagram?
3. What does the difference operation $(Z - Y)$ represent in a Venn diagram?
4. How can these set expressions be applied in real-life scenarios?
5. How do Cartesian products relate to set operations?

Tip: Always remember that intersections focus on common elements between sets, while unions combine all elements from the sets involved.