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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Please solve and prove the problem in short way.
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.
Transcribed Image 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.
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