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​

Answer 1

Answer:

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.