Subsets and Subspaces

Question

How does x+x=x, x+y=y, y+y=z ?

I do not understand how the U+W works out?

Suppose that U = {(x,x,y,y) F⁴}

W = {(x,x,x,y) F⁴}

theb U+W={9x,x,y,z) F⁴}

Answer 1

What is F⁴