Sets

\[\xi=\{1,2,\ldots,12\},\] \[A=\{1,2,3,4,5\},\quad B=\{4,5,6,7\},\quad C=\{2,4,6,8\}.\] Find:

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

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

3. \((A\cap C)\cup(B\cap C)\).

4. Compare your answers. State which expressions are equal and explain why parts (a) and (b) give different results.