Investigate!
  1. Find the cardinality of each set below.

    1. \(A = \{3,4,\ldots, 15\}\text{.}\)

    2. \(B = \{n \in \N \st 2 \lt n \le 200\}\text{.}\)

    3. \(C = \{n \le 100 \st n \in \N \wedge \exists m \in \N (n = 2m+1)\}\text{.}\)

  2. Find two sets \(A\) and \(B\) for which \(|A| = 5\text{,}\) \(|B| = 6\text{,}\) and \(|A\cup B| = 9\text{.}\) What is \(|A \cap B|\text{?}\)

  3. Find sets \(A\) and \(B\) with \(|A| = |B|\) such that \(|A\cup B| = 7\) and \(|A \cap B| = 3\text{.}\) What is \(|A|\text{?}\)

  4. Let \(A = \{1,2,\ldots, 10\}\text{.}\) Define \(\mathcal{B}_2 = \{B \subseteq A \st |B| = 2\}\text{.}\) Find \(|\mathcal{B}_2|\text{.}\)

  5. For any sets \(A\) and \(B\text{,}\) define \(AB = \{ab \st a\in A \wedge b \in B\}\text{.}\) If \(A = \{1,2\}\) and \(B = \{2,3,4\}\text{,}\) what is \(|AB|\text{?}\) What is \(|A \times B|\text{?}\)

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