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.
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The operation * on the set A = {1, 2, 3, 4, 5} is defined as
a * b = LCM of a and b.
2 * 3 = LCM of 2 and 3 = 6.
But 6 doesn't belongs to set {1,2,3,4,5}
take one more example ,
2 * 5 = LCM of 2 and 5 = 10
but 10 doesn't belongs to set {1,2,3,4,5}
similarly , when you can see 3*5 , 3*4 , 4*5 etc doesn't exist in set A = {1, 2 , 3 , 4 , 5 }
Therefore, the given operation * is not a binary operation.
a * b = LCM of a and b.
2 * 3 = LCM of 2 and 3 = 6.
But 6 doesn't belongs to set {1,2,3,4,5}
take one more example ,
2 * 5 = LCM of 2 and 5 = 10
but 10 doesn't belongs to set {1,2,3,4,5}
similarly , when you can see 3*5 , 3*4 , 4*5 etc doesn't exist in set A = {1, 2 , 3 , 4 , 5 }
Therefore, the given operation * is not a binary operation.
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