Assertion(A): The resistivity of a semiconductor increases with temperature
Reason (R): In a conducting solid, the rate of collisions between free electrons and ions increases with increases of temperature.

Resistivity of semiconductor decreases with temperature. The atoms of a semiconductor vibrate with large amplitudes at higher temperatures there by increasing conductivity not resistivity. Hence the given assertion is false.

And for a conductor, the rate of collisions between free electrons and ions increases with increases of temperature. Hence increasing the resistivity. So the given reason is a correct statement.