Step 1: Solve Question 9. Given the sets: $A = \{1, 2, 3\}$ $B = \{2, 3, 4\}$ $C = \{3, 4, 5\}$ Compute the number of elements in $A \cup B \cup C$, denoted as $|A \cup B \cup C|$. First, find the union of all three sets: $$A \cup B = \{1, 2, 3\} \cup \{2, 3, 4\} = \{1, 2, 3, 4\}$$ $$(A \cup B) \cup C = \{1, 2, 3, 4\} \cup \{3, 4, 5\}$$ $$A \cup B \cup C = \{1, 2, 3, 4, 5\}$$ Now, count the number of elements in the resulting set: $$|A \cup B \cup C| = 5$$ The answer for Question 9 is: $\boxed{5}$ Step 2: Solve Question 10. Given: Number of students enrolled in mathematics ($|M|$) = 100 Number of students enrolled in science ($|S|$) = 120 Number of students enrolled in both subjects ($|M \cap S|$) = 80 Find the number of students enrolled in at least one of the subjects, which is $|M \cup S|$. Use the Principle of Inclusion-Exclusion for two sets: $$|M \cup S| = |M| + |S| - |M \cap S|$$ Substitute the given values: $$|M \cup S| = 100 + 120 - 80$$ $$|M \cup S| = 220 - 80$$ $$|M \cup S| = 140$$ The answer for Question 10 is: $\boxed{140}$ Step 3: Solve Question 11. Given the sets: $A = \{1, 2\}$ $B = \{2, 3\}$ $C = \{3, 4\}$ a) Compute $(A \cup B) \cup C$ First, calculate $A \cup B$: $$A \cup B = \{1, 2\} \cup \{2, 3\} = \{1, 2, 3\}$$ Next, find the union of this result with $C$: $$(A \cup B) \cup C = \{1, 2, 3\} \cup \{3, 4\}$$ $$(A \cup B) \cup C = \{1, 2, 3, 4\}$$ b) Compute $A \cup (B \cup C)$ First, calculate $B \cup C$: $$B \cup C = \{2, 3\} \cup \{3, 4\} = \{2, 3, 4\}$$ Next, find the union of $A$ with this result: $$A \cup (B \cup C) = \{1, 2\} \cup \{2, 3, 4\}$$ $$A \cup (B \cup C) = \{1, 2, 3, 4\}$$ The answers for Question 11 are: *a) $\boxed{\{1, 2, 3, 4\}}$ *b) $\boxed{\{1, 2, 3, 4\}}$