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Question

# In a survey of 55 students, it was found that 25 had taken Mathematics 22 had taken Physics and 21 had taken Chemistry, 12 had taken Mathematics and Physics, 10 had taken Mathematics and Chemistry and 8 had taken Physics and Chemistry if 12 students had taken none of the three subjects to find the number of students, who had taken all the three subjects. Also, find the number of those who have taken (i) only Mathematics (ii) only Physics (iii) only Chemistry.

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Solution

## Let the set of students who took mathematics, physics and chemistry be represented by M, P and C respectively.n(U)=35n(M)=25n(P)=22n(C)=21n(MP)=12n(MC)=10n(PC)=8n(none)=12M∪P∪C=55−12=43M∪P∪C=n(M)+n(P)+n(C)−n(MC)−n(PC)−n(MP)+n(MPC)43=25+22+21−12−10−8+n(MPC)n(MPC)=5Only mathematics and physics : n(MP)−n(MPC)=7Only mathematics and chemistry : n(MC)−n(MPC)=5Only physics and chemistry : n(PC)−n(MPC)=3Only mathematics : n(M)−7−5+n(MPC)=25−12+5=18Only physics :n(P)−7−3+n(MPC)=22−10+5=17Only chemistry :n(C)−5−3+n(MPC)=21−8+5=18

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