= Solution
\b[$\mathcal E_1$ is a Dynkin system but not a pi-system.] The whole ten-point set has even cardinality, complements preserve parity, and disjoint unions of even sets are even. Two even sets can intersect in a singleton, for example $\{1,2\}$ and $\{2,3\}$.
\b[$\mathcal E_2$ is neither.] The infinite set $\mathbb N\setminus\{1\}$ belongs to it, but its singleton complement does not, so it is not a <Dynkin system>. The two infinite sets $\{1\}\cup\{2,4,6,\ldots\}$ and $\{1,3,5,\ldots\}$ intersect in the excluded singleton, so it is not a <pi-system>.
\b[$\mathcal E_3$ is a pi-system but not a Dynkin system.] Intersections of bounded open intervals are bounded open intervals or empty. However, the family does not contain the whole underlying set $\mathbb R$. None of the three families is a <sigma-algebra>.
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