Represent using Venn diagram in a class containing 32 students, a student

can either do Government or History or both. If 16 students do Government, 18 do History and 3 do none of the subjects, find how many do both

1 answer

Let's represent the information using a Venn diagram.

Assuming that A represents the set of students who do Government and B represents the set of students who do History, we can fill in the following information:
- The number of students who do Government (A) is 16.
- The number of students who do History (B) is 18.
- The number of students who do neither Government nor History is 3.

Now, let's find the number of students who do both Government and History (A ∩ B).

Using the formula for finding the number of elements in the union of two sets:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B), we can substitute in the known values:
32 - 3 = 16 + 18 - n(A ∩ B)
29 = 34 - n(A ∩ B)

Now, we can solve for n(A ∩ B):
n(A ∩ B) = 34 - 29 = 5

Therefore, 5 students do both Government and History.