The binary operation *′ on the set {1, 2, 3 4, 5} is defined as a *′ b = H.C.F of a and b.
The operation table for the operation *′ can be given as:
| * |
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 |
We observe that the operation tables for the operations * and *′ are the same. Thus, the operation *′ is same as the operation*
