A class has 50 students. 13 are juniors, 20 are psych majors, and 24 are neither psych majors nor juniors. How many psych majors are juniors?

To determine the number of psych majors who are juniors, we need to find the intersection between the group of juniors and the group of psych majors.

Given:
Total number of students (n) = 50
Number of juniors (A) = 13
Number of psych majors (B) = 20
Number of students who are neither psych majors nor juniors (C) = 24

We can use the principle of inclusion-exclusion to find the number of psych majors who are also juniors.

First, we find the number of students who are either juniors or psych majors by adding A and B:
A ⋃ B = A + B

Next, we subtract the number of students who are neither juniors nor psych majors. Let's call this set D:
n - C = A ⋃ B - D

We are interested in the intersection between the set of psych majors (B) and the set of juniors (A). We can find this intersection by subtracting set D from the union of A and B:
B ⋂ A = A ⋃ B - D

Substituting the given values into the equation, we get:
B ⋂ A = 13 + 20 - 24
B ⋂ A = 9

Therefore, there are 9 psych majors who are juniors.