#### Question

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.

#### 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?

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.