A state consisting of identical bosons labeled , , ..., must satisfy
where is an operator that permutes the particles. This defines a symmetric state. A state consisting of identical fermions labeled , , ..., must satisfy where is again an operator that permutes the particles. This defines an antisymmetric state. It is only possible to antisymmetrize a collection of single-particle states when all of the single-particle states are distinct -- this is the statement of the Pauli exclusion principle. The Pauli exclusion principle applies only to multi-fermion states i.e. it is possible to symmetrize a collection of single-particle states regardless of whether there is redundancy. Collecting all of this information, \begin{itemize} \item Bosons have symmetric wavefunctions. \item Fermions have antisymmetric wavefunctions. \item Bosons do not obey the Pauli exclusion principle. \item Fermions do obey the Pauli exclusion. \end{itemize} Therefore, answer (D) is correct. |

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