Let $$:$\{0,1\}\{0,1\}$ is a PRG$.$ We define $()=(),$ is $$ a PRF$?$ If yes, explain why; if not, give an explicit attack $($a PPT adversary that violates the definition$).(10$ pts$)$ In practice, it is often the case that good block ciphers such as AES $($or some carefully designed hashes such as SHA$256)$ are assumed to be a PRF$.$ However, block cipher, by name, works on a fixed length of blocks, e$.$g$.,$ AES works on $128-$bit messages only. The followings are two possible ways to adjust the input$/$output length of a PRF$,$ prove that the constructions are still PRF according to the above definition.