Question 144085
Plug in the truth values:

p=F
q=T
r=T

~q ↔ [ ~r ^ (p v q) ]

~T ↔ [ ~T ^  (F v T) ]

since ( F v T = T )

~T ↔ [ ~T ^ T ]

( ~T = F )

F ↔ [ F ^  T ]

( F ^  T = F )

F ↔ F

So this statement is true.