Given as "universe of discourse" the employees of a manufacturing plant/I> and (for purposes of insurance, etc.) the numbers are noted that are "wedded", "male", "skilled". The Venn diagram for this is:

                                                 PLANT
                        ______________________________________________________
                        |                                                     |
                        |   ____________________                              |                                                     |
                        |   |                   |                             |
                        |   |     WEDDED        |                             |
                        |   |           ________|____________________         |
                        |   |     1     |       |                    |        |
                        |   |           |   1   |    MALE            |        |
                        |   |           |       |                    |        |
                        |   |           |       |              3     |        |
                        |   |    _______|_______|________________    |        |
                        |   |    |  2   |  1    |               |    |        |
                        |   |____|______|_______|               |    |        |
                        |        |      |             4         |    |        |
                        |        |      |                       |    |        |
                        |        |      |_______________________|____|        |                                   
                        |        |                              |             |
                        |        |                              |             |
                        |        |                     3        |             |
                        |        |         SKILLED              |      5      |
                        |        |______________________________|             |                                
                        |                                                     |
                        |_____________________________________________________|

Conversely, given data about distribution in sets, the consistency of the report can be checked by the inclusion-exclusion algorithm. Given: TOTAL (in PLANT) = 20; N(wedded) = 5; N(male) = 9; N(skilled) = 10; N(wedded & male) = 2; N(wedded & skilled) = 3; N(male & skilled) = 5; N(wedded & male & skilled) = 1; N(single & female & unskilled) = 5. Then we have the formula:

N(wedded or male or skilled) = N(wedded) + N(male) + N(skilled) - N(wedded & male) - N(wedded & skilled)
- N(male & skilled) + N(wedded & male & skilled) = 5 + 9 + 10 - 2 - 3 - 5 + 1 = 15; N(Total) = N(wedded
or male or skilled) + N(sing & female & unskilled) = 15 + 5 = 20. The report is consistent.
(Note: This would not prove the report to be true. However, an inconsistent report cannot be
true. As Whitehead observed, we can only be sure of what is not so. In a fifty year period, I
have discovered many inconsistent reports issued by Government agencies, coroporation offices, etc. In
one college newspaper -- when it was found that the sum distributed in various categories was fewer than
those reported at the college -- the question was asked: "Are THEY here also?")