Question

A survey shows that 63% people watch news channel A whereas 76% watch news channel B. if x%

watch both the channels , prove that 39 ≤ ≤ 63.
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Answer 1

Answer:

Given n(A)=63% and n(B)=76%

⇒n(A∪B)=n(A)+n(B)−n(A⋂B)

⇒n(A∪B)=63+76−n(A⋂B)

Since n(A∪B)≤100

⇒63+76−n(A⋂B)≤100

⇒n(A⋂B)≥39

⇒x≥39

Generally n(A⋂B)≤n(A) and n(A⋂B)≤n(B)

⇒n(A⋂B)≤63 and n(A⋂B)≤76

Combining we get ;

⇒n(A⋂B)≤63

⇒x≤63

⇒39≤x≤63