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Standard IX

Mathematics

Venn Diagram

In a survey, ...

Question

In a survey, it was found that $21$ people liked product A, $26$ people liked product B and $29$ people liked product C. If $14$ people liked product 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.

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Solution

Number of peoples ho like $C$ only.
For only $C$
$n (C) - n (C \cap A) - n (N \cap C) + n (A \cap B \cap C)$
$\Rightarrow 29 {12 + 14} + 8$
$\Rightarrow 29 - 26 + 8$
$\Rightarrow 11$

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In a survey, it was found that 21 people liked product A, 26 people liked product B and 29 people liked product C. If 14 people liked product 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.

Number of peoples ho like C only.For only C n(C)−n(C∩A)−n(N∩C)+n(A∩B∩C)⇒29{12+14}+8⇒29−26+8⇒11

Number of peoples ho like $C$ only.
For only $C$
$n (C) - n (C \cap A) - n (N \cap C) + n (A \cap B \cap C)$
$\Rightarrow 29 {12 + 14} + 8$
$\Rightarrow 29 - 26 + 8$
$\Rightarrow 11$