[MOVED] Sets and set analysis  TOPIC_SOLVED

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

[MOVED] Sets and set analysis

Postby Malento on Tue Jun 07, 2011 2:14 am

There are three different cable channels namely NCC,CBB and NTK.In arecent survey of 560 viewers,it was found that 476 viewers responded to NTK,112 viewers to CBB and 168 viewers to NCC.112 viewers respond to exactly two channels and 28 to none.
Question.
i- Determine the number who responded to all the three cables
ii- Assuming 112 viewers respond to NCC and NTK, and 90 viewers respond to NTK and CBB, what is the number of viewers who watch only CBB?

I tried as follows:
i- Those who responded to all the three cables were 560-28 =532

ii- Please help in this answer.
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Postby stapel_eliz on Tue Jun 07, 2011 10:48 am

Malento wrote:There are three different cable channels namely NCC,CBB and NTK.In arecent survey of 560 viewers,it was found that 476 viewers responded to NTK,112 viewers to CBB and 168 viewers to NCC.112 viewers respond to exactly two channels and 28 to none.
Question.
i- Determine the number who responded to all the three cables
ii- Assuming 112 viewers respond to NCC and NTK, and 90 viewers respond to NTK and CBB, what is the number of viewers who watch only CBB?

I tried as follows:
i- Those who responded to all the three cables were 560-28 =532

Since 112 responded to "exactly" two (that is, to no fewer than two and to no more than two), then there cannot be 532 who responded to all three.

To learn how to work with Venn diagrams and the sets they represent, as well as how to interpret the words in the exercise, please study this lesson. :wink:
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