Question

Out of 500 car owners investigated, 400 owned cars A and 200 owned cars B : 50 owned both A and B cars. Is this data correct?

Answer 1

Hey !!

Let U be the set of car owners investigated. M be the set of persons who owned car A and S be the set of persons who owned car B.

Given that,

                 n (U) = 500 , n (M) = 400 , n (S) = 200 and n ( S ∩ M ) = 50

Then,

             n ( S ∪ M ) = n (S) + n (M) - n (S ∩ M) = 200 + 400 - 50 = 550

But S ∪ M ⊂ U implies n (S ∪ M) ≤ n (U).

This is a contradiction. So, the given data is incorrect.

GOOD LUCK !!