trying to track employee safety training by name and department

What I would like to be able to do is have a sheet that will give me a list, by department, of employees who have not completed their training to give to the manager of that department. I have on sheet 1 down the first column the department followed by each employee name,

across the top row I have the different topics for each safety training. I figured I would put a 'y' or 'n' in the grid to show if they have completed it. I am trying to make it so only the 'n' people show up, but I feel like I am making a lot of nested if statements.

I may be adding to many steps, I have an 'or' function after each department so that if any of the employees have an 'n' it will show that that department is not complete and then also at the end of each of the training columns I have an 'or' function that says if any of the departments show an 'n' I know that training is not complete.

My main problem is with Sheet 2, I want it to show the first set of training only if it is not complete, and if it is not complete I want to list the department followed by employees who have yet to complete the training. If the training is complete than it can just pass over that training and go to the next one. I have been making very long formulas using a lot of nested if statements but feel that may be too time consuming.

Is this something I can use a Database type formula for?

Attached is what I have tried to work on, on sheet two you can see that the first thing on there has a very long nested if formula and if I continue down that road I will have each cell having a formula that is representing every cell pretty much.