\documentclass[a4paper,12pt]{article}
\begin{document}
\parindent=0pt
QUESTION
Decide for each of the following statements whether or not it is
true giving a brief explanation of your answer.
\begin{description}
\item[(i)]
For each positive integer $n\geq2$ the symmetric group $S_n$ has a
subgroup of index 2.
\item[(ii)]
The function $f:D_n\longrightarrow Z_2$ defined by $f(g)=1$ if and
only if $g$ is a rotation (The set of rotations includes the
identity) and $f(g)=0$ if and only if $g$ is a reflection is a
homomorphism.
\item[(iii)]
There are precisely 48 elements in the cyclic group $Z_{180}$ with
the property that they each generate the whole group.
\item[(iv)]
Given any finite group $G$ there is a positive integer $n$ such
that $G$ is isomorphic to a subgroup of $S_n$.
\item[(v)]
Every group of even order is abelian.
\item[(vi)]
If $G$ is a finite group of order $n$ then $g^n=e$ for every
element $g\in G$.
\end{description}
ANSWER
\begin{description}
\item[(i)]
True, $A_n