Question-30030

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

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

57 students take physics (given) how many students take (i) physics (asked) ? Is inquired physics only? Please check the question, perhaps the data is not correct.

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

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

P:Set of physics holders n(P)=57 C:Set of chemistry holders n(C)=91 B:Set of biology holders n(B)=77 n(P∩C)=35 n(C∩B)=40 n(C−P−B)=14 n(C−P−B)=n(C)−n(C∩P)−(C∩B) +n(C∩P∩B) 14=91−35−40+n(C∩P∩B) n(C∩P∩B)=14+35+40−91=−2 But the number of elements must be nonnegative. Hence impossible case.

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

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