In a class of 36 student 25 study chemistry 22 study mathematics and 25 study physics,17 study physics and mathematics,18 study physics and chemistry and 15 study at least one of the three subject,find
a)Illustrate the information on the vendigram
First, let's recall what a Venn diagram is: it's a visual representation of the relationships between different sets, usually drawn as circles. In this problem, we have three sets: students who study Chemistry, Mathematics, and Physics. So we'll have three circles, one for each subject, and we'll label them as C, M, and P, respectively. The intersecting regions of the circles represent students who study more than one subject.
Now let's fill in the information given in the problem:
1. 25 students study Chemistry (C): this will be the total number of students in the C circle.
2. 22 students study Mathematics (M): this will be the total number of students in the M circle.
3. 25 students study Physics (P): this will be the total number of students in the P circle.
4. 17 students study Physics and Mathematics: this will be the intersecting region between the P and M circles.
5. 18 students study Physics and Chemistry: this will be the intersecting region between the P and C circles.
6. 15 students study at least one of the three subjects: since there are 36 students in class, that means 36 - 15 = 21 students study none of the subjects.
To fill in the remaining overlapping areas, we need to first find the number of students who study all three subjects. We'll do this by finding the total number of students in the overlapping areas, and then subtracting those that only study two subjects.
We are given that 17 students study Physics and Mathematics, 18 study Physics and Chemistry. Let's denote the number of students who study all 3 subjects as x. We can set up the following equation with the total number of students in the class (36):
25 (Chem) + 22 (Math) + 25 (Phys) - (17 + 18 - x) = 36
Solving for x, we get:
72 - 35 + x = 36
x = -1
However, since x is a negative number, we must have missed the number of students who study all three subjects when referencing the problem statement. Double-check the problem and ensure all numbers are accurate. If the numbers are correct, remember to place the number of students who study all 3 subjects in the center intersection of all 3 circles.