Is the following function is secure PRG?
Given F is a secure PRG and k is choosen random from key space K.
$G(x) = F(k,x) \oplus F(k,x \oplus 1^s)$
My solution - $x \oplus 1^s = x'$ so G(x) becomes $f \oplus f'$ with $f = F(k,x)$ and $f' = F(k,x')$. clearly f and f' are PRG i.e. generates random strings and $\oplus$ of these will be random.
Correct me if I am wrong.