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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:

  1. \(A \cup B\text{.}\)

  2. \(A \cap B\text{.}\)

  3. \(B \cap C\text{.}\)

  4. \(A \cap D\text{.}\)

  5. \(\bar{B \cup C}\text{.}\)

  6. \(A \setminus B\text{.}\)

  7. \((D \cap \bar C) \cup \bar{A \cap B}\text{.}\)

  8. \(\emptyset \cup C\text{.}\)

  9. \(\emptyset \cap C\text{.}\)

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