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Tuesday, 15 April 2014

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Answer
Let A, B, and C be the set of people who like product A, B, and C respectively.
n(A) = 21, n(B) = 26, n(C) = 29, n(A ∩ B) = 14, n(C ∩ A) = 12, n(B ∩ C) = 14, n(A ∩ B ∩ C) = 8
People who many liked product C only
= n(C) - n(C ∩ A) - n(B ∩ C) + n(A ∩ B ∩ C)
= 29 -12 – 14 + 8
= 11
Hence, 11 liked product C only.

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4 comments:

  1. Unknown26 January 2016 at 03:20

    Nice article very usefull thanks

    ReplyDelete
  2. Unknown9 September 2016 at 09:54

    Finally a answer i could understand i searched on other sites dont know what the hell were they doing in this question but here they explained it step by step.A really good place to know how to do it!!really good work keep it up

    ReplyDelete
  3. Winston23 February 2017 at 07:01

    Why should we add no. of people who liked all three products when it is asked to find no. of people who liked product C only.

    ReplyDelete