Need help with Venn diagram

Question

A survey of 239 SPC students was taken at registration. Of those surveyed:

1. 63 students had signed up for a Math course
2. 57 students had signed up for a Language Arts course
3. 32 students had signed up for a Humanities course
4. 15 students had signed up for both a Math and Language Arts course
5. 9 students had signed up for both a Math and Humanities course
6. 7 students had signed up for both a Language Arts and Humanities course
7. 3 students had signed up for all three courses

How many students had not signed up for any of these three courses?

Answer 1

draw a rectangle

inside the rectangle draw 3 overlapping circles

1 circle for math, 1 for language arts, 1 for humanities

calculate the total inside the 3 circles

subtract that from 239 to get how many didn't sign up for any of the 3 courses

it's over a hundred

one calculation is 115 didn't sign up for any of the 3

another adds to 112

at least one calculation has an error somewhere

but they both look about right, in the right range, with small margin of error