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Determine whether the operation is a binary operation or not
Given: Set \( S = \{1,2,3,4,5\} \) and operation defined by
\( a * b = \mathrm{LCM}(a,b) \)
Concept:
A binary operation must satisfy the closure property, i.e., the result must belong to the same set.
Solution:
Take \( a = 3 \), \( b = 4 \) from the set.
\( a * b = \mathrm{LCM}(3,4) = 12 \)
But:
\( 12 \notin \{1,2,3,4,5\} \)
Conclusion:
Since the result is not in the set, the operation is not closed.
❌ Therefore, the operation is NOT a binary operation on the given set.