= Solution
The <canonical anticommutation relations> give $\{a_1^\dagger,a_2^\dagger\}=0$, where each label includes both <momentum> and <spin>. Therefore
$$
|2,1\rangle=a_2^\dagger a_1^\dagger|0\rangle=-a_1^\dagger a_2^\dagger|0\rangle=-|1,2\rangle.
$$
Thus \b[exchanging the complete labels of the two identical <fermions> changes the sign of their state]. If the labels coincide, $(a_1^\dagger)^2=0$; the state vanishes, which is the <Pauli exclusion principle>. A negative state vector describes the same isolated physical ray, but its relative sign matters when exchange alternatives interfere.
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