
Problem 3.
Of a group of students who were entered in a math contest:
14 had taken algebra
(some of these may have also taken geometry, logic, or geometry and logic),
11 had taken geometry
(some of these may also have taken algebra, logic, or algebra and logic),
9 had taken logic
(some of these many also have taken algebra, geometry, or algebra and geometry),
6 students had taken both algebra and logic and geometry
(some of these may also have taken logic),
5 students had taken both algebra and logic
(some of these may also have taken geometry),
10 students had taken exactly two of these courses,
and 2 students had taken all three courses.
How many students had taken exactly one of these courses.
Solution:
Let A be the set of students who took algebra for which n(A) = 14
Let G be the set of students who took geometry for which n(G) = 11
Let L be the set of students who took logic for which n(L) = 9


