#### Answer

(a)
The least number of students who could have been taking both the courses can be shown in the Venn diagram as two disjoint sets shown below:
There is no intersection region in the Venn diagram. So, the least number of students who could have been taking both the courses is 0.

#### Work Step by Step

(b)
The greatest number of students who could have been taking both the courses can be shown in the Venn diagram as psychology is a subset of mathematics as follows:
So, the intersection region I contains 30 students, which can be the maximum number students who could have been taking both the courses.
(c)
The greatest number of students who could have been taking neither of the courses can be shown in the Venn diagram as psychology is a subset of mathematics as follows:
So, the region III represents the greatest number of students who have taken neither of the courses. Thus, the greatest number of students who could have been taking neither course is 60.