S1 = A ⊕ B and C1 = AB

S2 = S1 ⊕ C1

= ( A ⊕ B ) ⊕ AB

= (A ⊙ B). AB + (A ⊕ B). (AB)'

= (AB + A' B'). AB + (AB' + A' B). (A' + B')

= (AB ) + (AB' + A' B)

= (AB ) + (AB' + A' B) + AB

= A( B+B') + (A'+A) B = A + B

C2 = S1 . C1

= ( A ⊕ B ) . AB

= (AB' + A' B) . AB = 0