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प्रश्न
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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उत्तर
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
संबंधित प्रश्न
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If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[A \cup B \cup D\]
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Y = {y | y ∈ N, y is prime number from 1 to 20}
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P = {1, 3, 7, 10} then
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From the given diagram find :
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(ii) B - (A - C)
(iii) A - B
(iv) A ∩ B'
Is A ∩ B' = A - B?
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Represent the truth of the following statement by the Venn diagram.
No circles are polygons.
Represent the truth of the following statement by the Venn diagram.
All teachers are scholars and scholars are teachers.
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Express the truth of the following statement by the Venn diagram.
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