A survey shows that 63 % of the pepole watch a news channel whereas , 76 % watch an entertiament channel at a particular time If X% of the pepole watch both types of channels , then

Options

A. x= 35
B. `x ge 63`
C. `39 le x le 63`
D. x=39

Answer

C

Explanation

Let A be the set of those pepole who watch news channel and B be the set those people who watch entertainment channel then
c(A)= 63 , n(B) = 76 and `n( A cap B )= x `
`because n ( A cup B) le 100 `
`rArr n( A) +n(B) -m ( A cap B) le 100`
`rArr 63 + 76 -x le 100`
`rArr x ge 39 `
Also n(`A cap B) le` ` min .{ n( A) n ( B)}`
`rArr x le 63 `
`therefore 39 le x le 63`