We want to find the number of students that are not good in any of the courses.
There are 80 students.
45 are good in mathematics
15 are good in both, mathematics and in English
13 are good in both, mathematics and psychology
16 are good in both English and psychology
20 are good in psychology
9 are good in all of the courses.
First, we know that we have:
45 good in math + 20 good in psychology = 65 students good in something.
But we know that:
13 are good in both, mathematics and psychology
This means that there are 13 students that are being counted twice, so we need to subtract 13.
45 + 20 - 13 = 52 students good in something.
Now we know that:
15 are good in both, mathematics and in English
16 are good in both English and psychology
9 are good in all of the courses.
So one would want to also count these students, but notice that these are already good in mathematics or in psychology, so these are already counted.
And we can't see the number of students that are only good with English, so we can conclude that
52 students are good in something.
then 28 students are not good at any of the 3 courses.
If you want to learn more, you can read:
brainly.com/question/24350406
