SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION

Hi Folks,

Here is my case :

A company has 3 departments : VISA, Education & Reception

VISA : 300 employees
Education : 400 Employess
Reception : 450 Employees

30 employees belong to VISA & EDUCATION
40 employees belong to VISA & RECEPTION
50 employees belongs to RECEPTION & EDUCATION

20 employees belong to all three depts

Neither segment= 0

Working on the question how many employees belong at leat to 1 dept, I would like to understand one property I have noticed on the 3 sets case :

Number of employees belonging at least to 1 dept = VISA or /union EDUCATION or/union RECEPTION = 300 + 400 + 450 - 30 - 40 - 50 + 20 = 1050 employees.

In a 2 sets case, A, B, we know that A or / union B = A + B - A & / Intersection B = Segment A + Segment B + segment A&B

However, When I apply this concept on the 3 sets case above, I obtain different results using both formula (Union VS Segments addition), and UNION result > Segment sum result

UNION result - Segment addition result = 3 times Center segment value (VISA & EDUCATION & RECEPTION)

Obviously, there is something I miss, do not understand properly .... even if I know that I need to apply the union formula, I want to understand the difference between both approach, and when to use the segment one. From what I understand, the Segments addition gives me all different employees working in the company... so all employees working at least in one department ... doing so I miss 60 employees compared with the result of the UNION formula (respectively 990 and 1050)

Hope my case is crytal clear

Many thanks in advance for your great support on my question.

CHeers,