Consider a binary operation ∗ on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table 1.2).
(i) Compute (2 ∗ 3) ∗ 4 and 2 ∗ (3 ∗ 4)
(ii) Is ∗ commutative?
(iii) Compute (2 ∗ 3) ∗ (4 ∗ 5).
(Hint: use the following table)
Table 1.2
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Step-by-step explanation:
For every a,b \in\{1, 2, 3, 4, 5\} , we have a*b = b*a. Hence it is commutative.
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