A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like product B. what is the least number that must have liked both products?

Solution: Here, Number of consumers those like product A$\left(n\left(A\right)\right)=720$
Number of consumers those like product B$\left(n\left(A\right)\right)=450$
Number of elements in universal set $\left(n\left(U\right)\right)=1000$
We know, $n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$
Also, $n\left(A\cup B\right)\le n\left(U\right)$
So, the least number of consumers those like both products$\left(n\left(A\cap B\right)\right)=720+450-1000=170$