Question

The total no of students in a school are 100.55 of them take physics.65 of them opt maths.how many opt only physics??

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Answer 1

Let set A=no of students who opted physics (⇒n(A)=55) and
Let set B=no of students who opted maths.(⇒ n(B)=65).
Then ,
A U B=Total no of students.
Therefore , n(A U B)=100
Therefore , no.of students studying only physics=n(A-B)
Formula is:
n(A-B)= n(A U B) - n(B)
Or, n(A-B)=100-65
=35
Therefore , 35 students opted only physics (ANSWER)

Answer 2

let 
    n(A) =no.of students took physics = 55
    n(B) =no.of students took maths = 65
    n(A U B) = no.of students in the school = 100
    n (A П B) = no of students took both = n(A) + n(B) - n(A U B)
                                                         = 65 + 55 - 100
                                                         = 20
number students took only physics = n(A) - n (A П B)
                                                    = 55 - 20
                                                    = 35 students took only physics