Solution
= Solution
For every fixed $x_{1:n}$,
$$
(\mathcal H_1\cup\mathcal H_2)(x_{1:n})
=\mathcal H_1(x_{1:n})\cup\mathcal H_2(x_{1:n}).
$$
The cardinality of a union is at most the sum of the two cardinalities, so
$$
|(\mathcal H_1\cup\mathcal H_2)(x_{1:n})|
\leq s(\mathcal H_1,n)+s(\mathcal H_2,n).
$$
Taking the supremum over samples proves the <shattering coefficient of a union> bound
$$
\boxed{s(\mathcal H_1\cup\mathcal H_2,n)
\leq s(\mathcal H_1,n)+s(\mathcal H_2,n).}
$$