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

Question

Philoid · Accepted Answer

(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

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