On the set {0, 1, 2, 3, 4, 5}, a binary operation * is defined by a * b = a + b when a + b

Question

On the set {0, 1, 2, 3, 4, 5}, a binary operation * is defined by a * b = a + b when a + b < 6, and a * b = a + b - 6 when a + b ≥ 6. Which element acts as the identity for this operation?

Accepted Answer

0. For the identity e we need a*e=a. Since a+0=a<6 for every a in {0..5}, a*0=a. Hence 0 is the identity element.

On the set {0, 1, 2, 3, 4, 5}, a binary operation * is defined by a * b = a + b when a + b < 6, and a * b = a + b - 6 when a + b ≥ 6. Which element acts as the identity for this operation?

Solution

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