Something to be clarified about EM Wave: TE, TM and TEM

[NexusN]

I have been reading different articles about EM wave modes,
it is said that in TE waves the E_z is zero, similarly for TM H_z is zero, and TEM both E_z and H_z are zero.

How about the E_x and E_y in TE wave?
Someone said E_y is also zero and only E_x exists in TE...is this true? Is it possible that I overlooked some assumptions made?
Or actually the fact is, for TE, both E_x and E_y are NON-zero; only E_z is zero?

I know this is a simple question but I do hope to confirm it earlier and proceed with my study, thanks for your kind attention.

 

[swaha]

Please go through a textbook of UG level optics or electrodynamics & then in your problem specify what x,y,z directions mean.
You may refer Griffiths (electrodynamics), Hecht/ Ajay Ghatak (optics).