A Venn diagram is a graphical way to represent sets and their interactions. In this case, you would have two overlapping circles in your Venn diagram, one representing students who like Math and another representing students who like Biology.
1. To find how many students like both Math and Biology, we first need to know that every student likes at least one subject. That means the total of unique students liking either Math, Biology, or both is 50. However, if we add the students who like Math (27) and the students who like Biology (32), we get 59 which is higher than the total number of students. This excess count of 9 students is because we have counted the students who like both subjects twice. Hence, the number of students who like both Math and Biology is 9.
2. To find out how many students like Math alone, we subtract the number of students who like both subjects from the total number of students who like Math. So, 27 (the total number of students who like Math) - 9 (the students who like both) = 18 students like Math alone.
3. Similarly, to find out how many students like Biology alone, we subtract the number of students who like both subjects from the total number of students who like Biology. So, 32 (the total number of students who like Biology) - 9 (the students who like both) = 23 students like Biology alone.
In your Venn diagram, you would represent this by having total students as a rectangle, Math liking students as one circle within the rectangle, Biology liking students as another circle within the rectangle, and the overlap of the two circles representing the students who like both. You would then label the areas of the Venn diagram with the numbers we calculated: 18 (Math alone), 23 (Biology alone), and 9 (both).
