S_{0 = }A_{0 }xor ( B_{0 }xor K) xor C_{0}

C_{1 = }A_{0}(B_{0} xor K) + A_{0}C_{0 }+ (B_{0 }xor K).C_{0}

Now Since we can put only values for K and C_{0}. Therefore we can have 4 possible combinations of K and C_{0} ( 00,01,10,11). Putting these values in the above formula we get

1. K = 0 and C_{0} = 0 gives S_{0 }= A_{0 }xor B_{0 }and C_{1} = A_{0}.B_{0. }This shows A+B can be performed( Full Adder forumla modification by putting values of K and C_{0})

2. K = 1 and C_{0 }= 1 gives S_{0 }= A_{0 }xor B_{0 }and C_{1} = A_{0}.B_{0}' + A_{0 }+ B_{0}' . This shows A-B can be performed. ( Full Subtractor formula modification by putting values of K and C_{0.})

3. But to have A + 1 we need to put B = 0 and thats not allowed.

So option A is correct.