Let F be a PRF, how to prove F3 is PRF? Let $\operatorname{F}$ be a $\operatorname{PRF}$, how to prove $\operatorname{F^3_{k_1,k_2}}(x) = \operatorname{F_{k_1}}(x) \oplus \operatorname{F_{k_2}}(x) $ is aslo a $\operatorname{PRF}$?
This cannot be a PRF in all cases, because in the edge case where K1 = K2, the output of F3 will be 0 for all x.