How to show Sauer's Lemma when the inequalities are strict or they are equalities?

I have the following homework.

We proved Sauer's lemma by proving that for every class $$H$$ of ﬁnite VC-dimension $$d$$, and every subset $$A$$ of the domain,

$$\left|\mathcal{H}_{A}\right| \leq |\{B \subseteq A: \mathcal{H} \text { shatters } B\} | \leq \sum_{i=0}^{d}\left(\begin{array}{c}{|A|} \\ {i}\end{array}\right)$$

Show that there are cases in which the previous two inequalities are strict (namely, the $$\leq$$ can be replaced by $$<$$) and cases in which they can be replaced by equalities. Demonstrate all four combinations of $$=$$ and $$<$$.

How can I solve this problem?