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
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.
To represent this information using a Venn diagram, we can start by drawing two overlapping circles. Let's label one circle as "Government" and the other as "History".
According to the given information:
- 16 students do Government.
- 18 students do History.
- 3 students do none of the subjects.
Now, let's find the number of students who do both subjects:
To determine the number of students who do both subjects, we subtract the number of students who do each subject individually from the total number of students.
Total students = 32
Students who do Government only = 16
Students who do History only = 18
Students who do none = 3
So, let's calculate the number of students who do both:
Total students = Students who do Government only + Students who do History only + Students who do both + Students who do none
32 = 16 + 18 + Students who do both + 3
Rearranging the equation:
Students who do both = 32 - 16 - 18 - 3
Students who do both = 32 - 37
Since there cannot be negative students, we conclude that no students do both Government and History.
To represent this information using a Venn diagram, we can start by drawing two circles, one to represent the students who do Government and one for the students who do History. Since a student can do both subjects, there will be an overlapping area between the two circles.
Given that 16 students do Government (represented by circle G) and 18 students do History (represented by circle H), and 3 students do neither subject, we can fill in these numbers on the diagram.
The number of students who do both subjects can be calculated by subtracting the total number of students who do each subject separately from the total number of students.
Total number of students = 32 (given)
Number of students who do only Government = 16
Number of students who do only History = 18
Number of students who do both = Total number of students - (Number of students who do only Government + Number of students who do only History)
Number of students who do both = 32 - (16 + 18)
Number of students who do both = 32 - 34
Number of students who do both = -2
Since we cannot have a negative number of students, it seems there might be an error in the given information or calculation. Please double-check the information provided or clarify any missing details to continue.