We know that for 3 variables (A=0,B=1,C=1), f$_1$ = (A XNOR B XNOR C) = 1, since the input has even number of 1's.
But if we were to do this step by step, f$_2$ = (A XNOR (B XNOR C)) = (A XNOR (1 XNOR 1))
Now, 1 XNOR 1 = 1. So, f$_2$ = (A XNOR 1) = 0 XNOR 1 = 0.
Why is f$_1 \neq$ f$_2$ ?
Also, which is true : "XNOR operation gives a value of 1 for " : Even number of 1's in the input OR Even number of 0's in the input. (Sorry, but a certain professor implied the later, so have to confirm).