Answer to Question #278749 in Discrete Mathematics for feey

Question

From a total of 125 employees, 102 employees are assigned to perform ONLY ONE programming job, either system programming or application programming. And 10 employees are not assigned to perform any of those programming jobs. Overall, 52 employees are assigned to perform ONLY system programming jobs.

a. How many employees are assigned to perform both system programming jobs and application programming jobs?

b. How many employees are assigned to perform system programming jobs or application programming jobs?

c. How many employees are assigned to perform system programming jobs?

d. How many employees are NOT assigned to perform system programming jobs?

Answer 1

Let $A$ be an event that an employee is assigned to perform an application programming job and $S$ be an event that an employee performs a system programming job. The information above can be represented in the Venn diagram below.

Since 10 employees are not assigned to perform any of those programming jobs, we have 125-10=115 employees assigned to perform a programming job.

Since 102 employees are assigned to perform ONLY ONE programming job and  52 employees are assigned to perform ONLY system programming jobs then the number of employees assigned to perform ONLY application programming jobs is 102-52=50.

The number of employees assigned to perform both system and application programming is 115-102=13.

$a)$

The number of employees assigned to perform both system programming jobs and application programming jobs is 13.

$b)$

The number of  employees assigned to perform system programming jobs or application programming jobs is 50+52=102.

$c)$

The number of  employees assigned to perform system programming jobs is 13+52=65.

$d)$

The number of  employees NOT assigned to perform system programming jobs is 50.