Question

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people likes 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 1

Here
n(A)=a+b+c+d=21 ...(i)
n(B)=b+c+f+g=26 ...(ii)
n(C)=c+d+e+f=29 ...(iii)
$n(A\cap B)=b+c=14$ ...(iv)
$n(C\cap A)=c+d=12$ ...(v)
$n(B\cap C)=c+f=14$ ...(vi)
$n(A\cap B\cap C)=c=8$ ...(vii)



Putting value of c in (iv),(v) and (vi),
$b+8=14\Rightarrow b=6$
$8+d=12\Rightarrow d=4$
$8+f=14\Rightarrow f=6$
Putting value of c, d, f in (iii),
$8+4+e+6=29\Rightarrow e=29-18=11$
Number of people who like product C only =11.