Out of 32 people, 30 save paper and 14 people save plastic bottles. What is the total number of people who save both paper and plastic bottles? Assume all people save either paper or plastic bottles or both paper and plastic bottles.
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Correct answer: A. 12
Explanation
Let A = people who save paper (|A| = 30) and B = people who save plastic bottles (|B| = 14). Since every one of the 32 people saves at least one of the two, |A ∪ B| = 32. By inclusion-exclusion, |A ∩ B| = |A| + |B| - |A ∪ B| = 30 + 14 - 32 = 12. So 12 people save both.More Discrete Structures and Optimization questions
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