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Problem presentation

Problem presentation. Meng Li. Problem Set 3. #22:In a survey of 100 undergraduate math majors at a certain university, the following information is obtained about the courses they are taking during the spring semester: 41 are enrolled in real analysis

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Problem presentation

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  1. Problem presentation Meng Li

  2. Problem Set 3 • #22:In a survey of 100 undergraduate math majors at a certain university, the following information is obtained about the courses they are taking during the spring semester: • 41 are enrolled in real analysis • 44 are enrolled in differential equations • 48 are enrolled in linear algebra • 11 are enrolled in both real analysis and linear algebra • 14 are enrolled in both real analysis and differential equations • 19 are enrolled in both differential equations and linear algebra • 10 are not enrolled in any of these three courses • How many students are enrolled in all three of these courses?

  3. There are lots of information, what can we do? Venn diagram must be the best choice!

  4. Solution: See Blackboard ^-^

  5. Easy way to solve the problem: • The Principle of Inclusion-Exclusion: • If A1, A2, …, An are n≥2 finite sets, then: • ｜A1∪A2∪…∪An｜=∑1≤i≤n｜Ai｜-∑1≤i<j≤n｜Ai∩Aj｜+∑1≤i<j<k≤n｜Ai∩Aj∩Ak｜-… +(-1)n+1｜A1∩A2∩…∩An｜

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