Let F be a length$-$preserving pseudorandom function. For the following constructions of a keyed function F$$:$\{0,1\}^$ n $*\{0,1\}^$n$1->\{0,1\}^2$n$,$ state whether F$$ is a pseudorandom function. If yes, prove it; if not, show an attack F$\text{'}($x$)$: $=$F$(0||$ x$)||$ F$(0||$ x$)$

F$\text{'}($x$)$: $=$F$(0||$ x$)||$ F$(1||$ x$)$

F$\text{'}($x$)$: $=$F$(0||$ x$)||$ F$($x $||0)$

F$\text{'}($x$)$: $=$F$(0||$ x$)||$ F$($x $||1)$ give proper answer