Question: Suppose that for some language L we can always concatenate two words in L and get another word in L if and only if the

Suppose that for some language L we can always concatenate two words in L and get another word in L if and only if the words are not the same. That is, for any words w₁ and w₂ in L where w₁ ≠ w₂, the word w₁ w₂ is in L but the word w₁ w₁ is not in L. Prove that this cannot happen.

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