Question
Mathematics Question on Relations and Functions
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 |
Answer
(i) (2 * 3) * 4 = 1 * 4 = 1 2 * (3 * 4) = 2 * 1 = 1
(ii) For every a, b ∈{1, 2, 3, 4, 5}, we have a * b = b * a. Therefore, the operation * is commutative.
(iii) (2 * 3) = 1 and (4 * 5) = 1
∴ (2 * 3) * (4 * 5) = 1 * 1 = 1