# How many identities?

Algebra Level 3

Suppose $$S$$ is a set with a binary operation. Consider the following sentence about the identity elements in $$S$$:

$$S$$ has $$\underline{\phantom{1234567}}$$ left identities, $$\underline{\phantom{1234567}}$$ right identities, and $$\underline{\phantom{1234567}}$$ identity elements.

Which choice of words for the blanks gives a sentence that cannot be true?

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