Purple [Psi] (Air/Water) have effects which involve:
Memes (Air), Stories (Air), and Energies (Water)

in/to/from the:
Void (Air), Soul (Water), and Matrix (field)

Blue [Technology] (Air/Earth) have effects which involve:
Memes (Air), Stories (Air), and Structures (Earth)

in/to/from the:
Void (Air), Archive (Earth), and Matrix (field)

Purple (Air/Water) and Blue (Air/Earth) have and elemental conjuction (overlap) in the Air element. This means that a Purple/Blue deck will have effects which involve:

Memes (Air), Stories (Air), Energies (Water) and Structures (Earth)

in/to/from the:
Void (Air), Soul (Water), Archive (Earth), and Matrix (field)

a Purple/Blue (lacking the Fire element) deck will not able to effect:
Entities (Fire) or Avatar (Fire)
nor will it be able to effect anything in a Hand (Fire).

It can still remove/attack Entities (Fire) through combat, just not through card effects.

This deficit in the Fire element can be compensated for by using Frens (which can reach all 4 elements - their effects are generalized to "any card"), but this carries its own trade offs.

This deficit in the Fire element can also be compensated for by using Colorless cards (which have mono-element effects, and can be paid for by any single color, but are more expensive - also the colorless cards only give colorless energy, when played as an energy).