The correct option is
A increase as temperature is lowered
Conductivity should increase as the temperature is lowered because the bandgap in the metal is small and thus the electrons can easily take a leap to the conduction band and conduct electricity but with an increase in temperature, the thermal motion makes the electrons to collide and disturb the free flow.
Thus, conductivity is decreased. However, with a decrease in temperature, the thermal effect is nullified and the electrons can flow smoothly without hindrance and thus conductivity increases.
In semiconductors, the bandgap is big but small enough for few electrons to take a leap to the conduction band and conduct electricity to some extent.
However, with an increase in temperature, they get charged with thermal energy which is sufficient to overcome the energy barrier and leap to the conduction band and thus, their conductivity increases.
Hence, the correct option is A