Using the same sets from Example 1.37, perform the set operations indicated.

1. Find \(A \cap(B \cap C)\).

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

3. Find \(\left(A \cup C^{\prime}\right) \cap\left(B \cup C^{\prime}\right)\)

Data from Example 1.37

Perform the set operations as indicated on the following sets: \(U=\{0,1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{0,1,2,3,4,5,6\}, B=\{0,2,4,6,8,10,12\}\), and \(C=\{0,3,6,9,12\}\).

Find \((A \cap B) \cap C\).

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

Find \((A \cap B) \cup C^{\prime}\)