Which of the following statements is false?

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(A) set $G$ with a binary operation $\cdot$ is a group if it satisfies closure,associativity,identity,and inverse properties. For $(N, \cdot)$,where $

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$(N, \cdot)$ is a group

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(A) set $G$ with a binary operation $\cdot$ is a group if it satisfies closure,associativity,identity,and inverse properties. For $(N, \cdot)$,where $N$ is the set of natural numbers,the multiplicative inverse of an element $a \in N$ (where $a 
eq 1$) is $1/a$,which is not in $N$. Thus,$(N, \cdot)$ fails the inverse property and is not a group. $(N, +)$ is a semi-group because it is closed and associative under addition. $(Z, +)$ is a group as it satisfies all group axioms. The set of even integers $2Z = \{..., -4, -2, 0, 2, 4, ...\}$ forms a group under addition because it contains the identity $0$,inverses for all elements,and is closed and associative. Therefore,the statement $(N, \cdot)$ is a group is false.

$^*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$2$	$2$	$2$
$3$	$1$	$2$	$3$	$3$	$3$
$4$	$1$	$2$	$3$	$4$	$4$
$5$	$1$	$2$	$3$	$4$	$5$

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