= Solution
With the condition-first name convention used here, <evaluation of a forcing name> is
$$
\eta_G=\{\sigma_G:\exists p\in G\ ((p,\sigma)\in\eta)\}.
$$
Since a <generic filter> is nonempty, there is a condition in $G$. In the given <paired forcing name>, every condition is paired with both $\tau$ and $\tau'$, and there are no other lower-rank names. Therefore
$$
\boxed{\nu(\tau,\tau')_G=\{\tau_G,\tau'_G\}}.
$$
This is the \b[unordered pair] of the two interpreted sets. If the interpretations coincide, it is a singleton. It is neither an <ordered pair> nor the <set union> of those interpretations. Reversing the two components in the name-pair convention changes only the syntax of the same recursive evaluation.
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