Xy plane question.

[loli12]

Can R^2 be planes other than the xy plane if it is not defined?
Because I got this statement which the book claims it to be false.

Let W be the xy plane in R^3; that is, W={(a1, a2, 0):a1, a2 from R). R= field of real numbers. Then W=R^2.

is there any other reason to make this statement false?

 

[whozum]

R2 is just a two dimensional plane, you can put it anywhere you want.