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?

Answer 1

Number of elements in universal set`(n(AuuB)) = 500`
Number of elements in first set`(n(A)) = 400`
Number of elements in first set`(n(B)) = 200`
Number of elements in both sets`(n(AnnB)) = 50`
Now, we know,
`n(AuuB) = n(A) + n(B) - n(AnnB)`
`n(AuuB) = 400+200-50 = 550`
But, we are given, `n(AuuB) = 500`.
So, the data given is incorrect.