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Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication 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

(i)     Compute (2 * 3) * 4 and 2 * (3 * 4)
(ii)    Is * commutative ?
(iii)    Compute (2 * 3) * (4 * 5).

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