hello.

$\displaystyle (a);\left \{ (x,y)\in \mathbb{R}^{2},\exp x=\exp y\right \}$

i have to prove that $\displaystyle a$ is a subspace.

i took two elements from (a), $\displaystyle (x,y)$ and $\displaystyle (x',y')$ and i must have $\displaystyle (x+x',y+y')\in a$.

so i wrote $\displaystyle \exp (x+x')-\exp (y+y')=\exp x \exp x'-\exp y\exp y'$

where i went wrong ?

i know that $\displaystyle a$ can be written as $\displaystyle (a);\left \{ (x,y)\in \mathbb{R}^{2}, x= y\right \}$,but i want to know where was my error.

thanks.