# Tag Info

Your statement holds for all oracles $A$ iff $\mathsf{P} \neq \mathsf{NP}$. Indeed, if $\mathsf{P} \neq \mathsf{NP}$ then your statement vacuously holds. Conversely, if $\mathsf{P} = \mathsf{NP}$, then your statement fails for a random oracle $O$, since such an oracle satisfies $\mathsf{P}^O \neq \mathsf{NP}^O$ almost surely. A similar argument shows that ...