In a class of 104 students ,a student is allowed to offer economics or book keeping or geography both,35 students offered economics,43 offered book keeping,50 offered government,11 offered economic and government while 90 offered all the three subjects.
draw a Venn diagram for the students
how many students offered two subjects only
how many students offered one subject
To draw a Venn diagram for this scenario, you can start by drawing three overlapping circles that represent Economics, Bookkeeping, and Geography.
Label the circles accordingly:
Economics --> A
Bookkeeping --> B
Geography --> C
In the overlaps, write the numbers accordingly:
11 --> A ∩ C (students who offered Economics and Government)
90 --> A ∩ B ∩ C (students who offered all three subjects)
Now we can fill in the remaining numbers:
35 --> A - (A ∩ B ∩ C) (students who offered only Economics)
43 --> B - (A ∩ B ∩ C) (students who offered only Bookkeeping)
50 --> C - (A ∩ B ∩ C) (students who offered only Geography)
We can find the number of students who offered two subjects only by adding together the numbers in the overlapping regions:
(A ∩ B) + (A ∩ C) + (B ∩ C)
(A ∩ B) = 35 - (A ∩ B ∩ C)
(A ∩ C) = 11 - (A ∩ B ∩ C)
(B ∩ C) = 50 - (A ∩ B ∩ C)
Therefore, the number of students who offered two subjects only is:
(35 - (A ∩ B ∩ C)) + (11 - (A ∩ B ∩ C)) + (50 - (A ∩ B ∩ C))
For the number of students who offered one subject only, we need to add the numbers outside the overlapping regions:
(A - (A ∩ B ∩ C)) + (B - (A ∩ B ∩ C)) + (C - (A ∩ B ∩ C))
(A - (A ∩ B ∩ C)) = 35 - 90
(B - (A ∩ B ∩ C)) = 43 - 90
(C - (A ∩ B ∩ C)) = 50 - 90
Therefore, the number of students who offered one subject only is:
(35 - 90) + (43 - 90) + (50 - 90)
Simplifying these calculations will give you the final answers.