1. ## set theory

A salesman visits 274 housewifes in a town to find out their views about three products A,B and C. He finds that
157 use A,
9 use all three,
14 use A and C but not B,
39 use B and C,
48 use only B

(i) Which product is most popular according to this enquiry.
(ii) How many use product C only.

Please solve the problem and explain the steps.
thanks

2. It seems one information is missing to solve number a).
Do a Venn diagram.
You will find
$9 \in A \cap B \cap C$*
$14 \in A \cap C \setminus B$
$39 \in B \cap C$
You know that $9 \in A \cap B \cap C$ so you can deduce
$30 \in B \cap C \setminus A$
$48 \in B \setminus (A \cup B)$
You know that $157 \in A$ so
$144 \in (A \setminus (B \cup C)) \cup (A \cap B)\setminus (A\cap B\cap C)$
Finally $29 \in C \setminus A \cup B$