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Question
Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct?
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Solution
Let A be the set of people owned car A
Let B be the set of people owned car B
n(A) = 400, n(B) = 200, n(A ∩ B) = 50
n(A ∪ B) = 500 ...(1)
n(A) + n(B) – n(A ∩ B)
= 400 + 200 – 50
= 600 – 50
= 550 ...(2)
From (1) and (2) we get
n(A ∪ B) ≠ n(A) + n(B) – n(A ∩ B)
∴ The given data is not correct.
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