Question

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?

Answer 1

Pradeep's information is accurate as verified by applying the principle of inclusion-exclusion in set theory, confirming that the sum of employees with various skills matches the total number of employees.

Step-by-step explanation:

The question presented asks if Pradeep's reporting of information regarding the abilities of the employees is correct. To verify the correctness of the information, we use the principle of inclusion-exclusion in set theory.

We start by adding the number of employees who can cut tall trees (55) to those who can climb poles (50). However, this sum counts the 11 who can do both activities twice. To adjust for this, we subtract the 11 from our total. We also need to consider the 6 who can't do either activity. Therefore, the calculation becomes 55 + 50 - 11 + 6, which equals 100. This means the reported information matches the total number of employees. Thus, Pradeep's information is correct. By using the principle of inclusion and exclusion, we confirm that the reported numbers do add up.