digital logic - When do truth tables use the "Don't-care" term?

1. 
   

   In which situation can be used the Don't-care term?

   
   


2. 
   

   Suppose that I want to use 6 symbols: I need 3 bits, which in turn can generate 8 combinations. Since the last two combinations aren't useful in my case, should I put them to 0or Don't care?

   
   

This is the truth table of the useful symbols

0 0 0 | 1
0 0 1 | 0
0 1 0 | 0
0 1 1 | 1
1 0 0 | 0
1 0 1 | 1
------

The output of the combinations below doesn't exist, or it's irrelevant

1 1 0
1 1 1