The correct statement about the symmetry of the eigenfunctions of a quantum of 1-D harmonic oscillator is 

1
All the eigenfunctions are only even functions, because the potential is an even function.  
2
All the eigenfunction are only odd functions, although the potential is an even function.  
3
The eigenfunctions have no odd-even symmetry. 
4
All the eigenfunctions are either odd or even functions, because the potential is an even function. 
5
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