In a class of 45 students,30 read biology and 25 read chemistry. Each student reads at least one of the two subject
(i)illustrate this information on a venn diagram.
(ii) How many students read both subject
(iii) How many students read only chemistry
(iv) How many students read only one subject
(ii) 30+25-x = 40
Now make your Venn diagram, and the rest is easy
let B equal both
(ii) 30 + 25 - B = 45
(iii) 25 - B
(iv) 45 - B
(i) To illustrate this information on a Venn diagram, we can draw two overlapping circles representing Biology and Chemistry. Let's label the circle for Biology as A and the circle for Chemistry as B.
Biology (A)
[ 30 ]
| [ ]
|_______[ ]
|_________[________]
Chemistry (B)
[ 25 ]
(ii) To find the number of students who read both subjects, we need to find the overlapping region of the circles. From the diagram, we can see that the overlapping region represents the students who read both Biology and Chemistry. By counting the overlap, we can determine the number of students. In this case, it is 15.
(iii) To find the number of students who read only Chemistry, we need to find the portion of the circle B that does not overlap with circle A. From the diagram, we can see that the portion of circle B outside of the overlap represents the students who read only Chemistry. By counting this portion, we can determine the number of students. In this case, it is 10.
(iv) To find the number of students who read only one subject, we can subtract the number of students who read both subjects (15) and the number of students who read only Chemistry (10) from the total number of students (45).
Thus, the number of students who read only one subject is given by:
45 - 15 - 10 = 20.
To answer these questions, we can use the concept of Venn diagrams. A Venn diagram is a graphical representation that shows the relationship between different sets or groups. In this case, we will use a Venn diagram to represent the students who read biology and chemistry.
(i) Illustrating the information on a Venn diagram:
To create the Venn diagram, draw two intersecting circles. Label one circle "Biology" and the other circle "Chemistry."
Since 30 students read biology and 25 students read chemistry, write "30" in the area representing biology and "25" in the area representing chemistry.
(ii) Determining the number of students who read both subjects:
Look at the overlapping region of the circles (the intersection). This represents the students who read both biology and chemistry. Count the number of students in this region. Let's say there are "x" students who read both subjects.
(iii) Determining the number of students who read only chemistry:
To find the number of students who read only chemistry, subtract the number of students who read both subjects from the total number of students who read chemistry. So, 25 - x students read only chemistry.
(iv) Determining the number of students who read only one subject:
To find the number of students who read only one subject, add the number of students who read only biology and the number of students who read only chemistry. So, (30 - x) + (25 - x) students read only one subject.
Note: As mentioned in the question, each student reads at least one of the two subjects, which means no student reads neither biology nor chemistry.
By using the Venn diagram and the formulas derived above, you can determine the number of students who read both subjects, who read only chemistry, and who read only one subject.