1.Set Theory
easy

In a survey it was found that $21$ people liked product $A, 26$ liked product $B$ and $29$ liked product $C.$ If $14$ people liked products $A$ and $B, 12$ people liked products $C$ and $A, 14$ people liked products $B$ and $C$ and $8$ liked all the three products. Find how many liked product $C$ only.

A

$11$

B

$11$

C

$11$

D

$11$

Solution

Let $A, B$ and $C$ be the set of people who like product $A,$ product $B$, and product $C$ respectively.

Accordingly, $n(A)=21, n(B)=26, n(C)=29, n(A \cap B)=14, n(C \cap A)=12$

$n(B \cap C)=14, n(A \cap B \cap C)=8$

The Venn diagram for the given problem can be drawn as

It can be seen that number of people who like product $C$ only is $\{29-(4+8+6)\}=11$

Standard 11
Mathematics

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