Set Theory · Introduction

Lesson 9

Nikolai Chukhin · Alexander S. Kulikov

Problem. Check all set-theoretic identities (those equalities that hold for all \(A,B,C\)).

5 points

  1. \((A \cap B) \cup C = (A \cup C) \cap (B \cup C)\)

  2. \((A \cup B) \cap C = (A \cap C) \cup (B \cap C)\)

  3. \((A \cup B) \setminus C = (A \setminus C) \cup B\)

  4. \((A \cap B) \setminus C = (A \setminus C) \cap B\)

  5. \(A \setminus (B \cap C) = (A \setminus B) \cup (A \setminus C)\)