The relationship between the number of students that are good at a given subject is an illustration of sets.
We use the following representations:
[tex]M \to[/tex] Mathematics
[tex]E \to[/tex] English
[tex]P \to[/tex] Psychology
From the question, we have the following parameters
[tex]M = 45[/tex] -- Mathematics
[tex]M\ n\ E =15[/tex] -- Mathematics and English
[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology
[tex]E\ n\ P =16[/tex] -- English and Psychology
[tex]P=20[/tex] -- Psychology
[tex]All = 9[/tex] -- All 3 subjects
[tex]Total = 80[/tex] -- All students
The number of students that are good at mathematics only is as follows:
First, we calculate those that are good at mathematics and English only
[tex](M\ n\ E)' = M\ n\ E - All[/tex]
[tex](M\ n\ E)' = 15 - 9 = 6[/tex]
Then those that are good at mathematics and psychology only
[tex](M\ n\ P)' = M\ n\ P - All[/tex]
[tex](M\ n\ P)' = 13 - 9 = 4[/tex]
So, the students that are good at mathematics only are:
[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]
[tex]M' = 45 - 6 -4 -9[/tex]
[tex]M' = 26[/tex]
Hence, 26 students are good at Mathematics only.
To calculate the number of students that are not good in any of the subjects, we make use of the complement rule
[tex]A + A' = Total[/tex]
Where:
[tex]A \to[/tex] Students that are not good in any
[tex]A' \to[/tex] Students that are good in at least one
So, we have:
[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]
Where:
[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]
[tex](E\ n\ P) = 16-9 = 7[/tex]
The equation becomes:
[tex]A' =26 + 6 + 4+7+9[/tex]
[tex]A' =52[/tex]
Recall that:
[tex]A + A' = Total[/tex]
[tex]A = Total - A'[/tex]
[tex]A = 80 - 52[/tex]
[tex]A = 28[/tex]
Hence, 28 students are not good at all.
Read more about sets at:
https://brainly.com/question/24388608
