A composite symbol v/vf is used to analyse two staes (state v and state vf) quasi simultaneously. You can use boolean arithmetic on the left side and on the right side of the symbol and combine the results.
without fault v=vf, this is where 0/0 and 1/1 come from.
With fault, v<>vf, this is where 1/0 and 0/1 come from.
Example: correct state v=0, faulty state vf=1 -> v/vf=0/1 = /D (/D means D with overbar, I cannot write this here. it is only a symbolic name)
The short notation /D + 0 = 0/1 + 0/0 = 0/1 = /D means that all possible combinations are evaluated and re-combined into the resulting symbol.
if v=0 then V=0 + 0/0 results in 0 (since in both cases 0+0=0).
if vf=1 then Vf=1+0/0 results in 1 (regardless of the value of the second symbol 0/0, Vf=1 will lead to 1 at the output of "+").
Therefore the result is 0/1.
I recommend you go back to your training material and talk to fellow students. I'm not in a position to tutor you through this topic.