I know that {0,1}³ = {(0,0,0), (0,0,1), (0,1,0), (1,0,0), (1,1,0), (0,1,1), (1,0,1), (1,1,1)}. But how? Please clearly explain each step for expanding {0,1}³ into {(0,0,0), (0,0,1), (0,1,0), (1,0,0), (1,1,0), (0,1,1), (1,0,1), (1,1,1)}? That is the only part that I need help understanding.

The domain of relation C is {0, 1}. For x, y e{0, 113, xCy if y can be obtained from x by changing only one 0 to a 1