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A monoid becomes a group if it also satisfies the

\[\begin{array}{1 1}(1)closure\;axiom&(2)associative \;axiom\\(3)identity axiom&(4) inverse\; axiom\end{array}\]

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A monoid is a set satisfying
1) closure property
2) associative property
3) Existence of identify elements
If the above set satisfies existence of inverse then the monoid becomes a group.
Hence 4 is the correct answer.
answered May 22, 2014 by meena.p

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