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Is * Defined on the Set {1, 2, 3, 4, 5} by a * B = L.C.M. of a and B a Binary Operation? Justify Your Answer. - CBSE (Commerce) Class 12 - Mathematics

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Question

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

Solution

The operation * on the set A = {1, 2, 3, 4, 5} is defined as

a * b = L.C.M. of a and b.

Then, the operation table for the given 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

It can be observed from the obtained table that:

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

Hence, the given operation * is not a binary operation.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 8 | Page no. 25
Solution Is * Defined on the Set {1, 2, 3, 4, 5} by a * B = L.C.M. of a and B a Binary Operation? Justify Your Answer. Concept: Concept of Binary Operations.
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