Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.
(i) Compute (2 * 3) * 4 and 2 * (3 * 4)
(ii) Is * commutative?
(iii) Compute (2 * 3) * (4 * 5).
(Hint: use the following table)
| * |
1 |
2 |
3 |
4 |
5 |
| 1 |
1 |
1 |
1 |
1 |
1 |
| 2 |
1 |
2 |
1 |
2 |
1 |
| 3 |
1 |
1 |
3 |
1 |
1 |
| 4 |
1 |
2 |
1 |
4 |
1 |
| 5 |
1 |
1 |
1 |
1 |
5 |
