2. Let |A| = 12, |B| = 7,|C| = 9, and exactly 3 elements are common for A and B, exactly 5 elements are common for A and C, exactly 4 elements are common for B and C, and exactly 2 elements are common...

2. Please solve and prove the problem in short way.

Extracted text: 2. Let |A| = 12, |B| = 7,|C| = 9, and exactly 3 elements are common for A and B, exactly 5 elements are common for A and C, exactly 4 elements are common for B and C, and exactly 2 elements are common for A, B and C. How many elements could be in the union of the sets A, B and C? Prove your answer.