[.806] Question about Magic

So, I was playing around a bit and ran into the question of whether it was water or ice.. and then I began to wonder .

I had chosen water and air as my elemental books.  Did that combo give me ice magic?  If so, that would be cool..

Books Required = Access to Spells

Water + Air = Ice 

Water + Fire = Steam 

Water + Earth = Mud? 

Earth + Fire = Magma

Earth + Fire + Air = Obsidian

X_Element + Summoning = X_Elemental at L5

2X_Element + Summoning = More powerful critter at ~L8

I'd expect each element to have it's own strong 'flavor', such as Air having baseline spells like teleport and protection from range attack, but if you add earth, you can then learn spells like casting Sandstorm in the forest ..

Gracias.