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प्रश्न
Is the binary operation * defined on Z (set of integer) by m * n = m – n + mn ∀ m, n ∈ Z commutative?
उत्तर
No. Since for 1, 2 ∈ Z, 1 * 2 = 1 – 2 + 1.2 = 1 while 2 * 1 = 2 – 1 + 2.1 = 3 so that 1 * 2 ≠ 2 * 1.
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संबंधित प्रश्न
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 |
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