Question

A market research group conducted a survey of $2500$ consumers and reported that $1620$ consumers like product $p_1$ and $1500$ consumers like product $p_2$ then (Note $A$ and $B$ denotes the set of products $p_1$ and $p_2$ respectively)

• A. $n(A\cup B)\ge 620$
• B. $n(A\cap B)\le 1500$
• C. $620\le n(A\cap B)\le 1500$
• D. All of these

Answer 1

The correct option is D All of these

$n\left(A\right)=1620,n\left(B\right)=1500$

$\Rightarrow n(A\cap B)\le min\left\{n\right(A),n(B\left)\right\}$

$\Rightarrow n(A\cap B)\le 1500$

Also $n(A\cup B)\ge n\left(A\right)+n\left(B\right)-n\left(U\right)=620$

$n(A\cup B)\ge 620$

Hence all options are correct.