Using boolean algebra, it is easy to show that:
A xor B = (not A and B) or (A and not B)
A B | f = notA and B | g = A and notB | f or g | A xor B
----+----------------+----------------+--------+--------
0 0 | 0 | 0 | 0 | 0
0 1 | 1 | 0 | 1 | 1
1 0 | 0 | 1 | 1 | 1
1 1 | 0 | 0 | 0 | 0