Question: Example 2 . Find a set S with very few elements and a binary operation * on S such that * is associative and has

Example

2 .

Find a set S with very few elements and a binary operation

*

on S such that

*

is associative and has an identity element, but it is not the case that every element has an inverse with respect to this identity element. What is the least number of elements S can have?

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