auto populate (dates)

Please see the attached spreadsheet (auto populate)

I need the cells within Column C to auto populate depending on the value is of the adjacent cells within columns A and B.

If A3 is blank and B3 is blank – C3 needs to be blank
If A3 has a date in it and B3 has a date in it – C3 needs to equal whatever the most recent date is
If A3 has a date in it and B3 has N/A in it - C3 needs to equal A3
If A3 has a date in it and B3 is blank – C3 needs to be blank
If A3 is blank and B3 has a date in it – C3 needs to be blank

Please help!