class of 50 students, 27 study History, 27 Civics, 25 Economics, 15 History and Civics, 16 Civics and Economics. 14 History and Economics, 9 all the three. How many students study
Only Economics
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Step-by-step explanation:
History =27 (H)
Civics =27 (C)
Economics =25 (E)
History & Civics =15[H∩C]
Civics & Economics =16[C∩E]
History & Economics =14[H∩E]
9
study all
1) Only Economics =E−(H∩E)−(C∩E)+(H∩C∩E)
=25−16−4+9=4 (Answer)
2) Only Economics =4
So, Only History =27−15−14+9=7
& Only Civics =27−16−15+9=5
Total students who studies =4+7+5+H∩C+C∩E+H∩E−9−9−9
=−11+15+16+14
=4+16+14
=34
3) Studies Economics but not Civics =4+14−9=9
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