In a class of 80 students, 53 study Art, 60 study Biology, 36 study Art and Biology, 34 study Art and Chemistry, 6 study Biology only and 18 study Biology but not Chemistry. Illustrate the information on a Venn diagram. Determine the number of students who study
(I) Arts only
(ii) Chemistry
To start illustrating this information on a Venn diagram, let's label the three circles as "Art," "Biology," and "Chemistry."
First, we know that 53 students study Art, so we can place 53 inside the circle labeled "Art."
Next, we know that 60 students study Biology, so we can place 60 inside the circle labeled "Biology."
Then, we know that 34 students study Art and Chemistry, so we can place 34 inside the intersection of the Art and Chemistry circles.
We also know that 36 students study both Art and Biology, so we can place 36 inside the intersection of the Art and Biology circles.
Now, we know that 6 students study only Biology, which means they don't study any of the other subjects. We can place 6 in the section of the Biology circle that is outside of both the Art and Chemistry circles.
Similarly, we know that 18 students study Biology but not Chemistry, so we can place 18 in the section of the Biology circle that is outside of the Chemistry circle.
Lastly, we need to determine the number of students who study Arts only and Chemistry only. To do this, we can use the formula for finding the number in each section of the Venn diagram:
(Arts only) = (Art) - (Art and Biology) - (Art and Chemistry)
(Arts only) = 53 - 36 - 34
(Arts only) = 53 - 70
(Arts only) = -17
This result of -17 suggests that there may be an error in the given information. It is not possible for the number of students studying Art-only to be negative. Please double-check the information provided.