Question

A Market research group conducted a survey of 2000 consumers and reported that 1720 consumers liked product p₁ and 1450 consumers liked product $p_2$. Then the least number that must have liked both the products is

• A. 1070
• B. 930
• C. 420
• D. 1170

Answer 1

The correct option is D 1170

$n\left(\mu \right)=2000,n\left(A\right)=1720,n\left(B\right)-1450$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=3170-n(A\cap B)$
$SinceA\cup B<\mu ,n(A\cup B)\le n\left(\mu \right)$
$\Rightarrow 3170-n(A\cap B)\le 2000$
$\Rightarrow n(A\cup B)\ge 1170$