Students in the school of mathematics at a university major in one or more of the following four...
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Students in the school of mathematics at a university major in one or more of the following four areas: applied mathematics (AM), pure mathematics (PM), operations research (OR), and computer science (CS). How many students are in this school if (including joint majors) there are 23 students majoring in AM; 17 in PM; 44 in OR; 63 in CS; 5 in AM and PM; 8 in AM and CS; 4 in AM and OR; 6 in PM and CS; 5 in PM and OR; 14 in OR and CS; 2 in PM, OR, and CS; 2 in AM, OR, and CS; 1 in PM, AM, and OR; 1 in PM, AM, and CS; and 1 in all four fields.

Jan 24 2021 09:12 AM

1 Approved Answer

Sonia B
answered on
January 26, 2021

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Concept: |AM U PM U OR U CS| = |AM| + |PM| + |OR| + |CS| - |AM n PM| - |AM n OR| - |AM n CS| - |PM n OR| - |PM n CS| - |OR n CS| + |AM n PM n OR| + |AM n PM n CS| + |PM n OR n CS| + |AM n OR n CS| - |AM n PM n OR n CS|. Solution: Let AM denote the number of students measuring in applied mathematics, PM denote the number of students measuring in pure mathematics, OR denote the number of students measuring in operational research, CS denote the number of students measuring in computer science. It is given that |AM| =23,|PM| =17, |OR| =44 ,|CS| =63, |AM n PM| =5, |AM n OR| =4, |AM n CS| =8, |PM n OR| =5, |PM n CS| =6, |OR n...

| =14, |AM n PM n OR| =1, |AM n PM n CS| =1, |PM n OR n CS| =2, |AM n OR n CS| =2 and |AM n PM n OR n CS|=1. So, |AM U PM U OR U CS| = |AM| + |PM| + |OR| + |CS| - |AM n PM| - |AM n OR| - |AM n CS| - |PM n OR| - |PM n CS| - |OR n CS| + |AM n PM n OR| + |AM n PM n CS| + |PM n OR n CS| + |AM n OR n CS| - |AM n PM n OR n CS|=23+17+44+63-5-4-8-5-6-14+1+1+2+2-1 =153-87=66. Hence, the number of students in the school is 66.

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