A chain with more than two elements

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A chain with two elements $0$ & $1$ is complemented as complement of $0$ is $1$ and that of $1$ is $0$.How to show that every chain with more than two elements is not complemented?

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HINT: Suppose that $C$ is a chain and $x\in C\setminus\{0,1\}$. Let $y\in C$.

  • If $y\le x$, what is $x\lor y$?
  • If $x\le y$, what is $x\land y$?