Assume |s1|=|s2|=n and consider the functions defined, for any s1 and s2, as:
(a) G1(s1,s2)=s1 xor s2, (b) G2(s1,s2)=(s1, s2, s1 xor s2).
We have that:
A.
G1 and G2 are pseudo-random generators because their outputs are uniformly (and thus, pseudo-randomly) distributed if so are their input
B.
G1 and G2 are not pseudo-random generators because either their outputs are not longer than their inputs or there exists a statistical test that distinguishes their outputs from a random string of the same length
C.
G1 and G2 are not pseudo-random generators because either there exists an efficient algorithm that can compute their input from their output or their outputs are not longer than their inputs
D.
G1 and G2 can be proved to be pseudo-random generators using a proof by reduction