The operation * on the set A = {1, 2, 3, 4, 5} is defined as a * b = L.C.M. of a and b.
Then, the operation table for the given operation * can be given as:
| * |
1 |
2 |
3 |
4 |
5 |
| 1 |
1 |
2 |
3 |
4 |
5 |
| 2 |
2 |
2 |
6 |
4 |
10 |
| 3 |
3 |
6 |
3 |
12 |
15 |
| 4 |
4 |
4 |
12 |
4 |
20 |
| 5 |
5 |
10 |
15 |
20 |
5 |
It can be observed from the obtained table that
3 * 2 = 2 * 3 = 6 ∉ A,
5 * 2 = 2 * 5 = 10 ∉ A,
3 * 4 = 4 * 3 = 12 ∉ A,
3 * 5 = 5 * 3 = 15 ∉ A,
4 * 5 = 5 * 4 = 20 ∉ A
Hence, the given operation * is not a binary operation.
