Set Theory, Calendars, Clocks and Binomial Theorem

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Sets and Unions

    In a survey conducted to know people’s preference for android phones and I phones, 80 person preferred android phones while 60 person preferred I phones. There were 20 who liked both and may prefer any. If there was no one who didn’t prefer at least one of the phones,then on how many people was the survey conducted?
    1. 120
    2. 40
    3. 80
    4. 60


  • Correct Answer
    Choice A. 120

Detailed Solution

Diagrammatic Approach -

It is quite clear from the diagram that the number of people at the party were 60 + 20 + 40 = 120
Mathematical approach :
Let n(A) be the no. of persons that prefers android phones , the no of persons that prefers IOS be n(B) and n(A∩B) be the persons who liked both may prefer both.
Thus using the formula n(AUB) = n(A) + n(B) – n(A∩B)
n(AUB) = 80 + 60 – 20 = 120
Correct Answer: 120

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