A survey shows that 63% of the people watch news whereas 76% watch sports. If x% of people watch both sports and news, then
39≤x≤63
Let A be the set of percentage of those people who watch news and B be the set of percentage of those people who watch sports.
n(A)=63,n(B)=76,and n(A∩B)=x∵n(A∪B)≤100⇒n(A)+n(B)−n(A∪B)≤100⇒63+76−x≤100⇒x≥39Also, n(A∩B)≤min{n(A),n(B)}⇒x≤63∴39≤x≤63