question_answer 50)

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 anwser.  

Answer:

Let a = 2, b = 5 be two elements of {1, 2, 3, 4, 5}       Now, a * b = L.C.M. of a and b        2 * 5 = L.C.M. of 2 and 5 = 10             But 10        is not a binary operation on {1, 2, 3, 4, 5}.