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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.

Q. 7 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.

Answers (1)
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a * b = L.C.M. \;of \;a\; and \;b

A = \{1, 2, 3, 4, 5\}

Operation table is as shown below:

* 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

From the table, we can observe that

2*3=3*2=6 \notin A

2*5=5*2=10 \notin A

3*4=4*3=12 \notin A

3*5=5*3=15 \notin A

4*5=5*4=20 \notin A

Hence, the operation is not a binary operation.

 

 

 

 

 

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