Given sets A = 2, 3, 5, 7, B = 2, 3, 4, 5, 6, 7, 8, 9, and C = 1, 4, 9, 16, 25, 36, find (A ∪ B) ∩ C and (A ∩ B) ∪ C.

$$A \cup B = \{x \mid x \in A \text{ or } x \in B\}$$ $$A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9\}$$

The union of A and B is $\boxed{\{2, 3, 4, 5, 6, 7, 8, 9\}}$.

$$A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9\}$$ $$C = \{1, 4, 9, 16, 25, 36\}$$

$$(A \cup B) \cap C = \{x \mid x \in (A \cup B) \text{ and } x \in C\}$$

The common elements are 4 and 9.

$$(A \cup B) \cap C = \{4, 9\}$$

The intersection of $(A \cup B)$ and $C$ is $\boxed{\{4, 9\}}$.

$$A = \{2, 3, 5, 7\}$$ $$B = \{2, 3, 4, 5, 6, 7, 8, 9\}$$ $$A \cap B = \{x \mid x \in A \text{ and } x \in B\}$$

The common elements are $2, 3, 5, 7$.

$$A \cap B = \{2, 3, 5, 7\}$$

$$A \cap B = \{2, 3, 5, 7\}$$ $$C = \{1, 4, 9, 16, 25, 36\}$$ $$(A \cap B) \cup C = \{x \mid x \in (A \cap B) \text{ or } x \in C\}$$ $$(A \cap B) \cup C = \{1, 2, 3, 4, 5, 7, 9, 16, 25, 36\}$$

The union of $(A \cap B)$ and $C$ is $\boxed{\{1, 2, 3, 4, 5, 7, 9, 16, 25, 36\}}$.