A) 1150
B) 2000
C) 1170
D) 2500
Correct Answer: C
Solution :
[c]Let U be the set of all consumers who were questioned, A be the set of consumers who liked product \[{{P}_{1}}\] and B be the set of consumers who liked product \[{{P}_{2}}\]. |
It is given that \[n(U)=2000,n(A)=1720,n(B)\] |
\[=\,\,1450,\,\,n(A\cup B)=n(A)+n(B)-n(A\cap B)\] |
\[=1720+1450-n(A\cap B)\] |
\[=3170-n(A\cap B)\] |
Since, \[A\cup B\subseteq U\therefore n(A\cup B)\le n(U)\] |
\[\Rightarrow 3170-n(A\cap B)\le 2000\] |
\[\Rightarrow 3170-2000\le n(A\cap B)\] |
\[\Rightarrow n(A\cap B)\ge 1170\] |
Thus, the least value of \[n(A\cap B)\]is 1170. |
Hence, the least number of consumers who liked both the products is 1170. |
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