6.8.12 Set theory

Problem: Prove equalities using the properties of set operations and definitions of operations. Illustrate using EulerVenn diagrams. a) \( A \backslash B=A \Delta(A \cap B) \), b) \( (A \cup C) \times B=(C \times B) \cup((A \cap C) \times B) \cup(A \times B) \).