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Example 33 - Out of 500 car owners investigated, 400 owned car A

Example 33 - Chapter 1 Class 11 Sets - Part 2

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Example 33 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? Let the set of owners of car A & car B be A & B respectively Number of car A owned = n(A) = 400 Number of car B owned = n(B) = 200 Number of car A and car B owned = n(A ∩ B) = 50 We know that n (A ∪ B) = n (A) + n (B) – n (A ∩ B) = 200 + 400 – 50 = 550 So, number of people who owned either car A or car B = 550 But total number of car owners is only 500 (given in question) Number of people who own car A or car B should be less than total number of car owners investigated But, here 550 > 500 This is a contradiction. So, the given data is incorrect.

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