In certain class,12 students study history, 13 study government and 15 study Akan. Each student in the class study at least one of the three subjects, 6 students study two of the three subjects and 3 students study All three subjects. Find 1. The number of students who are in the class . 2. Those who study only one subject. 3 . Illustrate the information on the Venn diagram.
1. To find the number of students in the class, we can add the number of students who study each subject, and then subtract the number of students who study two or three subjects more than once:
12 + 13 + 15 - 6 - 3 = 31
Therefore, there are 31 students in the class.
2. To find the number of students who study only one subject, we need to subtract the number of students who study two or all three subjects from the total number of students:
31 - 6 - 3 = 22
Therefore, 22 students study only one subject.
3. The Venn diagram representing this information would have three circles overlapping in the center. The left circle would represent history, the right would represent government, and the bottom would represent Akan.
In the overlap between history and government, there would be 6 students. In the overlap between government and Akan, there would also be 6 students. In the overlap between history and Akan, there would be 6 students.
Finally, in the very center of all three circles, there would be 3 students.
The remaining areas of each of the three circles would represent the students who study each subject exclusively, with 6 students studying only history, 7 students studying only government, and 9 students studying only Akan.
To find the answers to your questions, let's use the information given step by step:
Step 1: Determine the total number of students who study at least one subject.
Based on the information given:
- 12 students study history
- 13 students study government
- 15 students study Akan
To find the total number of students who study at least one subject, we add up the number of students studying each subject:
12 + 13 + 15 = 40
So, there are a total of 40 students in the class.
Step 2: Determine the number of students who study only one subject.
To find the number of students who study only one subject, we need to subtract the number of students who study two or three subjects from the total number of students.
Given that 6 students study two of the three subjects and 3 students study all three subjects, we can calculate the number of students who study only one subject:
Number of students studying only one subject = Total number of students - (Students studying two subjects + Students studying three subjects)
Number of students studying only one subject = 40 - (6 + 3)
Number of students studying only one subject = 31
So, there are 31 students who study only one subject.
Step 3: Create a Venn diagram to illustrate the information.
To illustrate the information given, we can create a Venn diagram with three circles representing the subjects (history, government, and Akan) and their intersections.
Let's assign the letters H, G, and A to represent the number of students studying history, government, and Akan, respectively.
H = 12 (History students)
G = 13 (Government students)
A = 15 (Akan students)
Now let's fill in the intersections based on the information given:
- 6 students study two subjects: This means that there are 6 students in the intersections between two circles. We can place this number in the overlapping parts of the Venn diagram.
- 3 students study all three subjects: This means that there are 3 students in the overlapping region of all three circles.
- To find the number of students studying only one subject, we subtract the number of students in the intersections from the total number of students in each subject.
Using the numbers we calculated earlier:
Number of students studying only history = H - 6 - 3 = 12 - 6 - 3 = 3
Number of students studying only government = G - 6 - 3 = 13 - 6 - 3 = 4
Number of students studying only Akan = A - 6 - 3 = 15 - 6 - 3 = 6
Now we have all the information to create the Venn diagram:
H: 3
/ \
/ \
/ \
/ \
G: 4 A: 6
\ /
\ /
\ /
\ /
O: 6
The number inside each circle represents the number of students studying only that subject, and the number in the overlapping region represents the number of students studying multiple subjects.
So, to summarize:
1. The number of students in the class is 40.
2. There are 31 students who study only one subject.
3. The information is illustrated in the Venn diagram.