Question

in a survey it is found that 21 people like product A 21 people like product Band 24 like product C . If 14 people like product A and B 15 people like product B and C 12 people like product Cand A and 8people like all the three products Find?1) How many people are surveyed in all?2)How many like product C only

Answer 1

Answer:

Step-by-step explanation:

Let A, B and C denote the set of people who like products A, B and C respectively.

Then it is given that 21 people like product A, i.e. n(A) = 21.

Similarly, we have n(B) = 26 and n(C) = 29.

Now, 14 people like both A and B, so this means n(A \cap B) = 14.

Similarly, n(C \cap A) = 12, n(B \cap C) = 14 and n(A \cap B \cap C) = 8.

The number of people who liked just product C is given by =

n(C) – n(C \cap A) – n(B \cap C) + n(A \cap B \cap C)

( you can also create venn diagram for the same, the formula will be clearer in that case)

= 29-12-14+8

= 11.

Hence,11 people liked only product C.

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