6.8.6 Set theory

Problem: Prove set relations: a) \( A \cap B \subset A \cup B \); b) \( A \backslash(A \backslash B)=A \cap B \); c) \( A \backslash C \subset(A \backslash B) \cup(B \backslash C) \); d) \( A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \);