Could trees live without air

Trees are not make of air. They're made of wood, which is mostly cellulose.

However, we were all taught that trees take in carbon dioxide (one carbon atom for every two oxygen atoms) and release oxygen (pairs of oxygen atoms). This leaves the carbon atoms nowhere else to go but to form the tree itself. Thus the tree is indeed made of wood (mostly carbon) that was derived from a continual intake of molecules in the air.