A left identity element in a set is an element that, when used in a binary operation on any element of the set, leaves the other element unchanged. In this example, we will check if any of the elements in the set S = {a, b, c} acts as a left identity. Specifically, for an element e to be a left identity, the condition e * x = x must hold true for every element x in the set.
| a | b | c | |
|---|---|---|---|
| a | a | b | c |
| b | b | a | c |
| c | c | c | a |
| Condition | Result |
|---|---|
| e * x = x |