I think options are wrong . Above function will generate **C** as o/p :

The SOP equation : A'B'C + A'BC + AB'C + ABC = C(A'B' + A'B + AB' +AB) . which simply means on any combination of A and B the o/p generated is C.

Now the counter statements for the options:

A) **(ABC)'** **+ A'BC' + ABC **

ABC + (ABC)' = 1. Therefore , 1 + A'BC' = 1. That means this function will o/p 1 every time regardless of value of C which makes it wrong.

**B) A + B + C**

if A = 1 and B = 1 and C=0, then the equation becomes 1 + 1 + 0 = 1 . which is again wrong because value of C = 0 but the o/p generated is 1.

**C) A ⊕ B ⊕ C**

if A = 1 and B = 0 and C = 0, then the equation becomes 1 XOR 0 XOR 0 = 1 , which is again wrong because of C = 0 but the o/p generated is 1.

**D) AB + BC + CA**

if A = 0 and B = 0 and C = 1, then the equation becomes 0.0 + 0.1 +1.0 = 0, which is again wrong because of C = 1 but the o/p generated is 0.

any help will be appreciated