in class they are 55 students .22 study bible,15 study chemistry ,2,study mathematics, 20study both subject .1)calculate students study chemistry only 2)calculate student neither nor subject
To calculate the number of students who study chemistry only and the number of students who study neither subject, we can use the concept of sets and Venn diagrams. Let's go step by step.
Step 1: Set up the information in a Venn diagram:
Draw three overlapping circles to represent Bible, Chemistry, and Mathematics subjects. Label them accordingly.
Set A: Bible
Set B: Chemistry
Set C: Mathematics
Since 22 students study Bible, 15 study Chemistry, and 2 study Mathematics, write these numbers in the corresponding regions of the Venn diagram.
Step 2: Fill in the overlapping region:
We know that 20 students study both Bible and Chemistry. So, write 20 in the overlapping region of sets A and B.
Step 3: Calculate students who study Chemistry only:
To find the number of students who study Chemistry only, we need to subtract the number of students who study both Bible and Chemistry (20) from the total number of students studying Chemistry (15).
15 - 20 = -5
However, a negative value doesn't make sense in this context. Therefore, we conclude that there are 0 students studying Chemistry only.
Step 4: Calculate students who study neither subject:
To find the number of students who study neither Bible nor Chemistry nor Mathematics, we need to subtract the total number of students in all the sets from the total number of students in the class.
Total students in class = 55
Total number of students in sets A, B, and C = 22 + 15 + 2 = 39
Students who study neither subject = Total students in class - Total students in sets A, B, and C
55 - 39 = 16
Therefore, there are 16 students who study neither Bible nor Chemistry nor Mathematics.
In summary:
1) The number of students who study Chemistry only is 0.
2) The number of students who study neither Bible, Chemistry, nor Mathematics is 16.