A market research group conducted a survey of 2000 consumers and reported that 1720 consumers liked product `P_1` and 1450 consumers like product `P_2dot` What is the least number that must have liked both the products?

Explanation

Here, Number of consumers those like product A`(n(A)) = 720`

Number of consumers those like product B`(n(A)) = 450`

Number of elements in universal set `(n(U)) = 1000`

We know, `n(AuuB) = n(A)+n(B)-n(AnnB)`

Also, `n(AuuB) <= n(U)`

So, the least number of consumers those like both products`(n(AnnB)) =
720+450-1000 = 170`