Class 11

Math

JEE Main Questions

Sets

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?

Number of consumers those like product B$(n(A))=450$

Number of elements in universal set $(n(U))=1000$

We know, $n(A∪B)=n(A)+n(B)−n(A∩B)$

Also, $n(A∪B)≤n(U)$

So, the least number of consumers those like both products$(n(A∩B))=720+450−1000=170$