Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer

Solution:

The operation * on the set {1, 2, 3, 4, 5} is defined by a * b

= LCM of a and b.

The operation table for the operation *' can be given as:

* 1 2 3 4 5
1 1 2 3 4 5
2 2 2 6 4 10
3 3 6 3 12 15
4 4 4 12 4 20
5 5 10 15 20 5

3 * 2 = 2 * 3 = 6 ∉ A,

5 * 2 = 2 * 5 = 10 ∉ A,

3 * 4 = 4 * 3 = 12 ∉ A,

3 * 5 = 5 * 3 = 15 ∉ A,

4 * 5 = 5 * 4 = 20 ∉ A

The given operation * is not a binary operation

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.4 Question 7

Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer

Summary:

On observing the table shown in the solution * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b is a binary operation

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