I knew that $P \neq EXP$ by Time Hierarchy Theorem. But, I'd like to show that $P^A \neq EXP^A$ for all oracles A. How can I do it?
I knew that If I make A=EXP, PSPACE, NP, and many others, then this would show that the inequality holds. But, how can I prove it for all oracles? Can you give me hints?
Notes: I don't think that there exists some oracle that $P^B = EXP^B$ for some oracles B since it seems to me that $P \neq EXP$ using THT relativizes. But I don't know why it relativizes? Consider this as a minor question of the above question.