Identify the incorrect statements in the following description of Group 13 chemistry and provide corrections along with explanations of the principle or chemical generalization that applies:

(a) All the elements in Group 13 are nonmetals.

(b) The increase in chemical hardness on going down the group is illustrated by greater oxophilicity and fluorophilicity for the heavier elements.

(c) The Lewis acidity increases for BX₃ from X = F to Br and this may be explained by stronger Br–B π bonding.

(d) Arachno-boron hydrides have a 2(n + 3) skeletal electron count and they are more stable than nido-boron hydrides.

(e) In a series of nido-boron hydrides acidity increases with increasing size.

(f) Layered boron nitride is similar in structure to graphite and, because it has a small separation between HOMO and LUMO, it is a good electrical conductor.