Answer:
b) 24
Step-by-step explanation:
We solve building the Venn's diagram of these sets.
We have that n(S) is the number of succesful students in a classroom.
n(F) is the number of freshmen student in that classroom.
We have that:
[tex]n(S) = n(s) + n(S \cap F)[/tex]
In which n(s) are those who are succeful but not freshmen and [tex]n(S \cap F)[/tex] are those who are succesful and freshmen.
By the same logic, we also have that:
[tex]n(F) = n(f) + n(S \cap F)[/tex]
The union is:
[tex]n(S \cup F) = n(s) + n(f) + n(S \cap F)[/tex]
In which
[tex]n(S \cup F) = 58[/tex]
[tex]n(s) = n(S) - n(S \cap F) = 54 - n(S \cap F)[/tex]
[tex]n(f) = n(F) - n(S \cap F) = 28 - n(S \cap F)[/tex]
So
[tex]n(S \cup F) = n(s) + n(f) + n(S \cap F)[/tex]
[tex]58 = 54 - n(S \cap F) + 28 - n(S \cap F) + n(S \cap F)[/tex]
[tex]n(S \cap F) = 24[/tex]
So the correct answer is:
b) 24