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1 March, 12:52

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?

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  1. 1 March, 15:39
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    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
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