Prove that if A is a subset of B, then $\displaystyle <A>\leq <B>$.

Let $\displaystyle |A|=n \ \text{and} \ |B|=m$

$\displaystyle m\geq n$

$\displaystyle <A>=\{e,a,a^2,\cdots, a^{n-1}\}$

$\displaystyle <B>=\{e,b,b^2,\cdots, b^{m-1}\}$

Can I just since |A| less than or equal to |B|, <A> is a subgroup of <B>?