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,
\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.
Therefore, answer (D) is correct.