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Is * defined on the set {1, 2, 3, 4, 5} by a*b = LCM of a and

Question

Is $$ defined on the set {1, 2, 3, 4, 5} by $a b$ = LCM of a and b, a binary operation ? Justify your answer.

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Benjamin Discussed

*

defined on the set {1, 2, 3, 4, 5} by

a * b

= LCM of a and b, a binary operation ? Justify your answer.

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

We have

*

defined on the set {1, 2, 3, 4, 5} by

a * b =

LCM of a and b

Now,

3 * 4 = 12

But

12

is not in set {1, 2, 3, 4, 5}.

Hence,

*

is not a binary operation.

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Question Text	Is $$ defined on the set {1, 2, 3, 4, 5} by $a b$ = LCM of a and b, a binary operation ? Justify your answer.
Answer Type	Text solution:1
Upvotes	150