Question

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked
product C ,14 people liked products A and B. 12 people like C and A,15 people like B and C
and 8 liked all the three products . Find how many liked product C only​

Answer 1

Answer:

Step-by-step explanation:

Our question is: In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked

product C ,14 people liked products A and B. 12 people like C and A,15 people like B and C

and 8 liked all the three products .

Our aim is to find how many liked product C only​.

Firstly we need to consider all possible cases, so lets organize them correctly:

• 21 people liked product A
• 26 people liked product B
• 29 liked C
• 14 liked A and B
• 12 liked A and C
• 15 liked B and C

Since we want to find the number of people who liked only product C, let consider n to be the number of people involved, n = 117.

From 117 people we have that 29 liked product C, in this sentence we can not say that it is only for product C, then we need to exclude the cases that are not only for product C, that is:

29 - 12 - 15 = 2

Hence, the number of people who only liked the product C was 2.

I hope this helped in your studies!!

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Answer 2

Answer:

Step-by-step explanation:

a,b,c,d belongs to all of set A (including the ones shared with other sets)

b,c,e,f belongs to all of set B (including the ones shared with other sets)

c,d,f,g belongs to all of set C (including the ones shared with other sets)

a + b + c + d = 21

b + c + e + f = 26

c + d + f + g = 29

b + c = 14, c + f =15, c + d = 12

c = 8

d = 4, c = 8, f = 7, b = 6 g = 10, e = 5, a = 3

like product c only = g = 10