Question

Out of 600 car owners investigated, 500 owned car A, 200 owned car B and 50 owned both A and B cars. Verify whether the given data is correct or not.

Answer 1

Let P and Q be the sets of those who own car A and car B respectivelty. Then,
` n(P)=500, n(Q) =200 and n( PcapQ)=50`.
Now , `n(Pcup Q) =n(P) +n(P) +n(Q) -n(Pcap Q)`.
`rArr n(PcupQ)=(500 +200-50)=650`.
This is a contradiction , since the maximum value of `n(Pcup Q) is 600`.
Hence , the given data is incorrect.