I was confused by what it means when a Random variable is a deterministic function of another Random variable yet is independent of it ? .How is this possible?

Here's the question . Consider three random variables X,Y and Z such that Z is independent of X and of Y and is a deterministic function of (X,Y). Is H(Z)=0 ? If so prove it ; if not , give a counter example 
                   
Thanking You