Consider the following circuit. Which one of the following is TRUE?

Derivation: express the signals from the left NAND gates and the final NAND.

The two left gates are NANDs with outputs NOT(X AND Y) and NOT(Y AND Z).

The final gate is a NAND taking those two outputs, so

f = NOT( NOT(X AND Y) AND NOT(Y AND Z) ).

Apply De Morgan's law:

f = (X AND Y) OR (Y AND Z) = Y AND (X OR Z).

• X is not redundant: set Y = 1, Z = 0 → f = X.

• Z is not redundant: set Y = 1, X = 0 → f = Z.

• Y is not redundant: set X = 1, Z = 0 → f = Y.

Conclusion: Each of X, Y, Z can change the output in some input assignment, so none of X, Y, Z is redundant.