A marketing report concerning personal computers states that 650,000 owners will buy a printer for their machines next year and 1,250,000 will buy at least one software package. If the report states that 1,450,000 owners will buy either a printer or at least one software package, how many will buy both a printer and at least one software package?

450,000 will buy both a printer and at least one software package

Explanation:

A (size 650,000) is the set of printer buyers

B (size 1,250,000) is the set of software buyers

(A or B) (size 1,450,000) is the set of people buying either a printer or software package.

(A and B) is the set of people buying both a printer and at least one software package

According to the inclusion-exclusion principle in set theory, we have:

(A or B) = A + B - (A and B)

So (A and B) = A + B - (A or B) = 1,250,000 + 650,000 - 1,450,000 = 450,000