In a certain discrete math class, three quizzes were given. Out of the 30 students in the class: 15 scored 12 or above on quiz #1,
12 scored 12 or above on quiz #2,
18 scored 12 or above on quiz #3,
7 scored 12 or above on quizzes $\# 1$ and $\# 2$,
11 scored 12 or above on quizzes $\# 1$ and $\# 3$,
8 scored 12 or above on quizzes #2 and #3,
4 scored 12 or above on quizzes $\# 1$, #2, and #3.
(a) How many scored 12 or above on at least one quiz?
(b) How many scored 12 or above on quizzes 1 and 2 but not 3?

Question

In a certain discrete math class, three quizzes were given. Out of the 30 students in the class: 15 scored 12 or above on quiz #1,
12 scored 12 or above on quiz #2,
18 scored 12 or above on quiz #3,
7 scored 12 or above on quizzes $\# 1$ and $\# 2$,
11 scored 12 or above on quizzes $\# 1$ and $\# 3$,
8 scored 12 or above on quizzes #2 and #3,
4 scored 12 or above on quizzes $\# 1$, #2, and #3. 
(a) How many scored 12 or above on at least one quiz?
(b) How many scored 12 or above on quizzes 1 and 2 but not 3?

Quizplus · Accepted Answer

The Answer is 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 \cap B ) = 7 , N ( A \cap C ) = 11

,

N ( B \cap C ) = 8

, and

N ( A \cap B \cap C ) = 4

. Then

N ( A \cup B \cup 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.

In a Certain Discrete Math Class, Three Quizzes Were Given #1\# 1#1

In a Certain Discrete Math Class, Three Quizzes Were Given $\# 1$