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Which of the following is not a group?

\[\begin{array}{1 1}(1)(Z_{n}.+_{n})&(2)(Z,+)\\(3)(Z,.)&(4)(R,+)\end{array}\]

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$(Z,.)$ is not a group since for $a \notin Z=> a$ is an integer its multiplicative inverse is $\large\frac{1}{a}$ which is not an integer i.e $\large\frac{1}{a} \notin Z$
$(Z,.) $ is not a group
Hence 3 is the correct answer.
answered May 22, 2014 by meena.p
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