1. The problem asks to shade specific set operations on three overlapping sets A, B, and C inside a universal set. 2. Recall the set operation definitions: - Intersection $A \cap B$ is elements in both A and B. - Union $A \cup B$ is elements in A or B or both. - Complement $A'$ is elements not in A. 3. For each part, we identify the region in the Venn diagram: (a) $A \cap B$: Shade the overlap of circles A and B. (b) $A \cup C$: Shade all areas in A or C. (c) $A \cap (B \cap C)$: Shade elements in A and also in the intersection of B and C. (d) $(A \cup B) \cap C$: Shade elements in C that are also in A or B. (e) $B \cap (A \cup C)$: Shade elements in B that are also in A or C. (f) $A \cap B'$: Shade elements in A but not in B. (g) $A \cap (B \cup C)'$: Shade elements in A that are not in B or C. (h) $(B \cup C) \cap A$: Same as (g) but order reversed, shade elements in A and also in B or C. (i) $C' \cap (A \cap B)$: Shade elements in the intersection of A and B but not in C. (j) $(A \cup C) \cup B'$: Shade elements in A or C or not in B. (k) $(A \cup C) \cap (B \cap C)$: Shade elements that are in A or C and also in both B and C. 4. Each shading corresponds to the described set region in the Venn diagram with three circles inside the universal set rectangle. 5. This exercise helps understand intersections, unions, and complements visually in set theory. Final answer: The shaded regions correspond exactly to the set expressions given in parts (a) through (k).