Random generation from Two Pseudo-Random Generators of Unknown Seed Given outputs from two pseudo-random generators with a non-equal, unknown seed, to which any basic opperation is applied, will the final result be undiscernable from a random number?  
Consider, for example, two options (a & b). To achive a fair result, two people draw the options on a sheet of paper. The first person may rotate it 180° while the second one is blinded. Then, still without seeing, the latter chooses between left or right.
Is that output (1|0) random? Or is it affected by pseudorandomness?
 A: Assume that the options $0$ and $1$ are written on a piece of paper deterministically, say, with $0$ on the left and $1$ on the right (with both observers having the same viewpoint).  Let $A$ be the event that the first observer rotates the paper (so that $0$ is now on the right and $1$ is now on the left) and let $\overline{A}$ be the event that the first observer does not rotate the paper.  Let $B$ be the event that the second observer chooses the left option and let $\overline{B}$ be the event that the second observer chooses the right option, with events $B$ or $\overline{B}$ independent of events $A$ or $\overline{A}$ (because the second observer is blindfolded).
For $0$ to be chosen, (event $\overline{A}$ and event $B$) or (event $A$ and event $\overline{B}$) must occur.  Note that $\overline{A}\cap B$ and $A\cap\overline{B}$ are disjoint (that is, they cannot happen at the same time).  The event that $0$ is chosen is $(\overline{A}\cap B)\cup(A\cap\overline{B})$ and it happens with a probability $P(\overline{A})P(B)+P(A)P(\overline{B})$.
Similarly, the event that $1$ is chosen happens with a probability $P(A)P(B)+P(\overline{A})P(\overline{B})$.

Now to your main question.  If events $A$ and $B$ are pseudo-random, then that means that if the seeds are known, then the events and the outputs are known with certainty beforehand, that is, the output is not random, that is, it is neither pseudo-random nor truly random.
If the seeds are unknown, we say that the output is pseudo-random (and not truly random) because it can be determined if the seeds were known.
