Let, x1⊕x2⊕x3⊕x4 = 0 where x1, x2, x3, x4 are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE ?
(A) x1x2x3x4 = 0
(B) x1x3+x2 = 0
(C) x′1⊕x′3=x′2⊕x′4
(D) x1+x2+x3+x4 = 0
Answer: (C)
Explanation: First we rearrange the terms,
x1⊕x2⊕x3⊕x4 = 0
x1⊕x3⊕x2⊕x4 = 0
x1⊕x3 = x2⊕x4
Then use a⊕b=a′⊕b′a⊕b=a′⊕b′ to get (C).
x′1⊕x′3=x′2⊕x′4
Another approach :
You can take a counter example to disprove other options.
You can take x1 = x2 = x3 = x4 = 1.
Only option (C) is correct.