Exercise
Which of the following structures is a semi-group?
Z with operation a * b = ab + 3
Z with operation a * b = 3(a + b)
Z with operation a * b = 3ab
No, (1 * 1) * 2 = 4 * 2 = 11 and 1 * (1 * 2) = 1 * 5 = 8.
No, (1 * 1) * 2 = 6 * 2 = 24 and 1 * (1 * 2) = 1 * 9 = 30.
Yes, this operation is associative.