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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 - Mathematics

Sum

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.

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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 ∩ B) = 14, n(C ∩ A) = 12,

n(B ∩ C) = 14, n(A ∩ B ∩ 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

Concept: Venn Diagrams
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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.7 | Q 16 | Page 27
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