Solve the problem.
-A survey of 134 college students was done to find out what elective courses they were taking. Let A = the set of those taking art, $B =$ the set of those taking basketweaving, and $C =$ the set of those taking canoeing. The study revealed the following information.
$\begin{array} { l l }
n ( A ) = 45 & n ( A \cap B ) = 12 \
n ( B ) = 55 & n ( A \cap C ) = 15 \
n ( C ) = 40 & n ( B \cap C ) = 23 \
n ( A \cap B \cap C ) = 2
\end{array}$
How many students were not taking any of these electives?
A)52
B)10
C)44
D)42

Question

Solve the problem.
-A survey of 134 college students was done to find out what elective courses they were taking. Let A = the set of those taking art, $B =$ the set of those taking basketweaving, and $C =$ the set of those taking canoeing. The study revealed the following information.
$\begin{array} { l l } 
n ( A ) = 45 & n ( A \cap B ) = 12 \
n ( B ) = 55 & n ( A \cap C ) = 15 \
n ( C ) = 40 & n ( B \cap C ) = 23 \
n ( A \cap B \cap C ) = 2
\end{array}$
 How many students were not taking any of these electives?
A)52
B)10
C)44
D)42

Quizplus · Accepted Answer

Using the principle of inclusion-exclusion, the number of students taking at least one elective is calculated as: $ n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C) = 45 + 55 + 40 - 12 - 15 - 23 + 2 = 92 $. Therefore, the number of students not taking any electives is $ 134 - 92 = 42 $.

Solve the Problem B=B =B= The Set of Those Taking Basketweaving, And

Solve the Problem $B =$ The Set of Those Taking Basketweaving, And