Addition of either trivalent or pentavalent impurities to an intrinsic semiconductor increases its conductivity.
A) True
B) False

Hint: The conductivity of a semiconductor depends upon the presence of free charge carriers. More number of free charge carriers means electric charge (and hence current) can be carried easily and hence, the conductivity will be more. Trivalent and pentavalent impurities give rise to free charge carriers.

Complete step-by-step answer:
In a semiconductor, electric charge and hence, electric current is carried by free charge carriers. If free charge carriers are more in number, electric current can flow easily and conductivity of the semiconductor increases.
An intrinsic semiconductor is made up of purely one element which has a valence shell with 4 valence electrons (such as silicon and germanium). These 4 valence electrons bond with 4 valence electrons of their neighboring atom to complete their octet. Therefore, since the electrons are bound, there is a deficit of free charge carriers.
Pentavalent impurities (like P,As) have 5 electrons in their valence shell. When they are added to an intrinsic semiconductor, 4 electrons of the pentavalent atom bond with 4 electrons of the atom of the semiconductor to form an octet. Thus, one electron remains free and becomes a free charge carrier. This increases the conductivity of the intrinsic semiconductor.
Trivalent impurities (like Ga, In) have 3 valence electrons in their outer shell. When added to intrinsic semiconductors, the 3 electrons try to bond with 4 electrons by breaking bonds and jumping between two electrons. This results in a void in one of the bonds at all times. This void is known as a hole. Since it is a deficit of electrons, it acts as a positive free charge carrier. This also increases the conductivity of the intrinsic semiconductor.
Hence, it is true that addition of either trivalent or pentavalent impurity to an intrinsic semiconductor increases its conductivity.
Hence, the correct option is A) True.

Note: Students must not think that only electrons are considered charge carriers in semiconductors and hence, since only pentavalent impurities provide extra electrons, only they increase conductivity. Holes are also considered free charge carriers, as movement of electrons in one direction leads to movement of holes in the other direction, that is, in essence, they carry positive charge in a direction opposite to the negative charge carried by the electrons. Therefore, trivalent impurities also increase the conductivity of an intrinsic semiconductor by providing for the formation of holes in the semiconductor.