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Question Number 30030 by mondodotto@gmail.com last updated on 15/Feb/18

Commented by Rasheed.Sindhi last updated on 15/Feb/18

$$57\mathrm{students}\mathrm{take}\mathrm{physics}\left(\mathrm{given}\right)$$$$\mathrm{how}\mathrm{many}\mathrm{students}\mathrm{take}\left(\mathrm{i}\right)\mathrm{physics}\left(\mathrm{asked}\right)$$$$?$$$$\mathrm{Is}\mathrm{inquired}\mathbf{physics}\mathbf{only}?$$$$\mathrm{Please}\mathrm{check}\mathrm{the}\mathrm{question},\mathrm{perhaps}\mathrm{the}$$$$\mathrm{data}\mathrm{is}\mathrm{not}\mathrm{correct}.$$

Commented by mondodotto@gmail.com last updated on 15/Feb/18

$$\mathrm{please}\mathrm{help}\mathrm{this}\mathrm{question}$$

Answered by Rasheed.Sindhi last updated on 16/Feb/18

$$\mathrm{P}:\mathrm{Set}\mathrm{of}\mathrm{physics}\mathrm{holders}$$$$\mathrm{n}\left(\mathrm{P}\right)=57$$$$\mathrm{C}:\mathrm{Set}\mathrm{of}\mathrm{chemistry}\mathrm{holders}$$$$\mathrm{n}\left(\mathrm{C}\right)=91$$$$\mathrm{B}:\mathrm{Set}\mathrm{of}\mathrm{biology}\mathrm{holders}$$$$\mathrm{n}\left(\mathrm{B}\right)=77$$$$\mathrm{n}(\mathrm{P}\cap \mathrm{C})=35$$$$\mathrm{n}(\mathrm{C}\cap \mathrm{B})=40$$$$\mathrm{n}(\mathrm{C}-\mathrm{P}-\mathrm{B})=14$$$$\mathrm{n}(\mathrm{C}-\mathrm{P}-\mathrm{B})=\mathrm{n}\left(\mathrm{C}\right)-\mathrm{n}(\mathrm{C}\cap \mathrm{P})-(\mathrm{C}\cap \mathrm{B})$$$$+\mathrm{n}(\mathrm{C}\cap \mathrm{P}\cap \mathrm{B})$$$$14=91-35-40+\mathrm{n}(\mathrm{C}\cap \mathrm{P}\cap \mathrm{B})$$$$\mathrm{n}(\mathrm{C}\cap \mathrm{P}\cap \mathrm{B})=14+35+40-91=-2$$$$\mathrm{But}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{elements}\mathrm{must}\mathrm{be}$$$$\mathrm{nonnegative}.$$$$\mathrm{Hence}\mathrm{impossible}\mathrm{case}.$$

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