Lecture 11 - Exercises
Part A - Proofs with Sets
- Prove that \(\{12n : n \in \mathbb{Z}\}
\subseteq \{2n: n \in \mathbb{Z}\} \cap \{3n: n \in
\mathbb{Z}\}\).
- Suppose \(A, B,\) and \(C\) are sets. Prove that if \(B \subseteq C\), then \(A \times B \subseteq A \times C\).
- Supoose \(A, B,\) and \(C\) are sets. Prove that \(A \cap (B \cup C) = (A \cap B) \cup (A \cap
C)\).
- Prove that if \(A\) and \(B\) are both sets with universal set \(U\), then \(\overline{A \cap B} = \overline{A} \cup
\overline{B}\).