In a certain discrete math class, three quizzes were given. Out of the 30 students in the class:

Question

Answer 1

a. Let A, B, and C be the sets of all students who scored 12 or above on quizzes #1, #2, and
#3, respectively. Then N(A) = 15,N(B) = 12, N(C) = 18, N(A ? B) = 7, N(A ? C) = 11,
N(B ? C) = 8, and N(A ? B ? C) = 4. Then
N(A ? B ? C) = 15 + 12 + 18 ? 7 ? 11 ? 8 + 4 = 23.
So 23 students scored 12 or above on at least one quiz.
b. The number of students who scored 12 or above on quizzes 1 and 2 but not 3 is 7 ? 4 = 3.