First slide

Operations on Sets

Question

A boating club consists of $82$ members,
each member is either a sailboat owner or a powerboat
owner. If $53$ members owned sailboats and $38$ members
owned powerboats, the number of members owned both
sailboat and powerboat is

Moderate

A

6
B

7
C

9
D

4

Solution

Let $S =$ the set of all members owning sailboats
and $P =$ the set of all members owning powerboats
$n (S \cup P) = n (S) + n (P) - n (S \cap P)$
$82 = 53 + 38 - n (S \cap P)$
$\Rightarrow n (S \cap P) = 91 - 82 = 9 .$

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