Question

120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology class (B). If 37 of them are signing up for both Math and Biology, how many are signing up for neither Math nor Biology. Hint: It may help to draw the Venn diagram, None of the other choices is correct. 37 13 93 43

Answer 1

To find the number of students signing up for neither Math nor Biology, we can subtract the number of students signing up for both from the total number of students. So, the number of students signing up for neither Math nor Biology is 93.

Step-by-step explanation:

To solve this problem, we can use the principle of inclusion-exclusion. We know that 80 students are signing up for Math, 50 students are signing up for Biology, and 37 students are signing up for both Math and Biology.

To find the number of students signing up for neither Math nor Biology, we can subtract the number of students signing up for both from the total number of students.

So, the number of students signing up for neither Math nor Biology is 80 + 50 - 37 = 93.

Answer 2

To find the number of students who are not signing up for Math or Biology, we subtract the total number of students in either class from the total number of students, adding back those who were counted in both classes. The answer is 27 students.

Step-by-step explanation:

To determine how many students are signing up for neither Math (M) nor Biology (B) when we know that 120 students are signing up for classes, 80 for Math, 50 for Biology, and 37 for both, we use the principle of inclusion-exclusion from set theory. The formula to calculate the number of students not in either class is the total number of students minus the sum of students in each class plus the number of students in both classes:

Total students = Students in M + Students in B - Students in both M and B

Number of students in neither = Total students - (Students in M + Students in B - Students in both M and B)

So we have:

Number of students in neither = 120 - (80 + 50 - 37) = 120 - 93 = 27

Therefore, 27 students are signing up for neither class.