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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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