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



(i) (2 3) 4 = 1 * 4 = 1

2 (3 4) = 2 * 1 = 1


(ii) For every a, b ϵ {1, 2, 3, 4, 5},


We have, a * b = b * a


the operation * is commutative.


(iii) (2 3) = 1


(2 3) (4 * 5) = 1 * 1 = 1


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