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From data base perspective it's called self join. You would do a left join to the same table with different alias and join employee with vendor. What Tableau can do is it will match row to row, but not scan entire list of vendors and determine if one employee matches at least one vendor or vice versa.
Instead of data modeling or joins outside tableau here is what you can do
1. Duplicate the datasource.
2. Left join two tables with keys being employee and vendor
3. Create a calculated field Employee (from left table)=vendor (from right table)
If it is a match it's true.
I have created a workbook with sample data on Tableau Public. You may ignore If you have already tried this.
Thanks Peter for replying this question. What you answered is the table join approach I was referring to.
Since there is no other answers, it seems like this is the only way to solve this problem.