Solution
= Solution
{c}
For $W=aH$ and $W'=bH$, define
$$
f:W\to W',\qquad f(w)=ba^{-1}w.
$$
If $w=ah$ then $f(w)=bh\in bH$, so this <function> is well defined. Its <inverse function> is $w'\mapsto ab^{-1}w'$, since successive left <translation in a group> by $ba^{-1}$ and $ab^{-1}$ cancels. Thus
$$
\boxed{f:aH\xrightarrow{\sim}bH\text{ is a bijection}.}
$$
In particular every left <coset> has the same <cardinality> as $H$.