There are 8 building blocks for ~q <-> [~r^(pvq)] 
so that each successive one can be gotten by
doing negation, disjunction, conjunction, and 
biconditional operations on one or two previous
building blocks, starting with the single letters: 
  
        ~q <-> [~r^(pvq)]            
                                 
1                   p                start with 1st single letter
2        q                           2nd single letter
3                r                   3rd single letter
4               ~r                   the negation of 3
5                  (pvq)             the disjunction of 1,2
6              [~r^(pvq)]            the conjunction of 4,5
7       ~q                           the negation of 2
8       ~q <-> [~r^(pvq)]            the biconditional of 6 and 7

Make a chart:

 p    q   r   ~r   (pvq) [~r^(pvq)]   ~q    ~q <-> [~r^(pvq)]
 |    |   |    |     |      |          |        |   
 F    T   T    F     T      F          F        T

So the truth value is T.

Edwin