Exercise 24.

Let \(X = \{n \in \N \st 10 \le n \lt 20\}\text{.}\) Find examples of sets with the properties below and very briefly explain why your examples work.

  1. A set \(A \subseteq \N\) with \(|A| = 10\) such that \(X \setminus A = \{10, 12, 14\}\text{.}\)

  2. A set \(B \in \pow(X)\) with \(|B| = 5\text{.}\)

  3. A set \(C \subseteq \pow(X)\) with \(|C| = 5\text{.}\)

  4. A set \(D \subseteq X \times X\) with \(|D| = 5\)

  5. A set \(E \subseteq X\) such that \(|E| \in E\text{.}\)

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