Explanation : Mathematically, XOR is both associative and commutative ie.
If C = A XOR B then B = C XOR A or B = A XOR C and
and A = B XOR C A = C XOR B
Explanation : The output f = (x+x')+(y+y').
Starting derivation using 'f'.
-->(x+x')+(y+y')
-->(x+y)+(x'+y')
-->(Already a known Input)+(x'+y')
So, the unknown input is (x'+y'). This can be made by :-
x and y fed into a NOT gate and then AND gate to become (x'+y').
So the answer is NAND gate.