Let \(A = \{1, 2, 3, 4, 5, 6\}\text{,}\) \(B = \{2, 4, 6\}\text{,}\) \(C = \{1, 2, 3\}\) and \(D = \{7, 8, 9\}\text{.}\) If the universe is \(\U = \{1, 2, \ldots, 10\}\text{,}\) find:
\(A \cup B\text{.}\)
\(A \cap B\text{.}\)
\(B \cap C\text{.}\)
\(A \cap D\text{.}\)
\(\bar{B \cup C}\text{.}\)
\(A \setminus B\text{.}\)
\((D \cap \bar C) \cup \bar{A \cap B}\text{.}\)
\(\emptyset \cup C\text{.}\)
\(\emptyset \cap C\text{.}\)