Question

in a survey of 65 students it was found that 25 had taken maths,22 had taken physics ,21 had taken chemistry ,12 had taken maths and physics ,8 had taken physics and chemistry ,12 had taken non of these .find only maths,physics,chemistry find using venn diagram​

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

Answer 2

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