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, find the number of students, who had taken all the three subjects.
Also find the number of Those have taken (I ) only Mathematics (ii) only physics (iii) only chemistry

Answer 1

Step-by-step explanation:

Let the set of students who took mathematics, physics and chemistry be represented by M, P and C respectively.

n(U)=35

n(M)=25

n(P)=22

n(C)=21

n(MP)=12

n(MC)=10

n(PC)=8

n(none)=12

M∪P∪C=55−12=43

M∪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)=5

Only mathematics and physics : n(MP)−n(MPC)=7

Only mathematics and chemistry : n(MC)−n(MPC)=5

Only physics and chemistry : n(PC)−n(MPC)=3

Only mathematics : n(M)−7−5+n(MPC)=25−12+5=18

Only physics :n(P)−7−3+n(MPC)=22−10+5=17

Only chemistry :n(C)−5−3+n(MPC)=21−8+5=18

solution

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