Statement I: If the temperature of a semiconductor is increased, then its resistance decreases.

Statement II: The energy gap between conduction band and valence band in a semiconductor is very small.

In semiconductors the energy gap between conduction band and valence band is small ($\approx$ 1 eV).  Due  to temperature rise, electron  in the valence band gained thermal energy and may jump across the small energy gap, goes in to the conduction band. Thus conductivity increases and hence resistance decreases.