Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.
(i). Compute (2 * 3) * 4 and 2 * (3 * 4)
(ii). Is *commutative?
(iii). Compute (2 * 3) * (4 * 5).
(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 2 1 1 5

Solution:

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

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

ii. For every a, b ∈ {1, 2, 3, 4, 5} , we have a * b = b * a.

Therefore, * is commutative.

iii. (2 * 3) * (4 * 5)

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

Therefore

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

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.4 Question 4

Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.
(i). Compute (2 * 3) * 4 and 2 * (3 * 4) (ii). Is *commutative? (iii). Compute (2 * 3) * (4 * 5). (Hint: Use the following table)

Summary:

For the given binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table, * is commutative and (2 * 3) * (4 * 5) = 1 * 1 = 1