Question

In a class of 100students, 55students have passed in Mathematics and 67
students have passed in physics.
Then the number of students who have passed in physics only is??


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Answer 1

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Let M and P be the sets of the students who passed Mathematics and Physics respectively.

Here,

n(U)=100

n(M)=67

n(P)=55

Since, all students have passed n(U)=n(M∪P)=100

Now,

n(M∪P)=n(M)+n(P)−n(M∩P)

or, 100=67+55−n(M∩P)

or, n(M∩P)=122−100=22

Now, set of students who only passed in Physics denoted by n

∘

(P)=n(P)−n(M∩P)

n

∘

(P)=55−22=33

Therefore, number of students passed in Physics only =33.

Answer 2

Answer:

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