Question
Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table 1.2).
Compute (2 * 3) * 4 and 2 * (3 * 4)
(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

2 * 3 = 1 and 3 * 4 = 1
Now (2 * 3) * 4 = 1 * 4 = 1 and 2 * (3 * 4) = 2 * 1 = 1

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