Pradeep is a Section Chief for an electric utility company. The employees in his section cut down tall trees or climb poles. Pradeep recently reported the following information to the management of the utility.
Out of 100 employees in my section, 55 can cut tall trees, 50 can climb poles, 11 can do both, 6 can't do any of the two. Is this information correct?

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Solution

Given: No of employees $(ξ) = 100$
No employees who can cut trees $= n (A) = 55$
No of employees who can climb poles $= n (B) = 50$
No of employees who can do both $= n (A \cap B) = 11$
No of employees who can't do any of the two $= n (A \cup B)^{'} = 6$
Now,
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 55 + 50 - 11 = 94$
or
$n (A \cup B) = ξ - n (A \cup B)^{'}$
$= 100 - 6 = 94$
Since, in both ways $n (A \cup B)$ values are same, the information given is correct.

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