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.
Solution:
The operation * on the set A = {1, 2, 3, 4, 5} is defined as
a * b = L.C.M. of a and b.
Then, the operation table for the given operation * can be given as:
It can be observed from the obtained table that:
$3 * 2=2 * 3=6 \notin A, 5^{*} 2=2 * 5=10 \notin A, 3^{*} 4=4^{*} 3=12 \notin A$
$3 * 5=5^{*} 3=15 \notin A, 4 * 5=5 * 4=20 \notin A$
Hence, the given operation * is not a binary operation.
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