When given the same input, do the following functions always produce the same output?

Option $1$:

def check$\_$function$($x$,$ y$,$ z$)$:

return x $==2$ or y $==1$ or z $==0$

Option $2$:

def check$\_$again$($x$,$ y$,$ z$)$:

if x $==2$:

if y $==1$:

return True

else:

return False

else:

return False

Group of answer choices

The functions above will not run due to a syntax error.

The functions above will produce the same output for all arguments.

The functions above will produce different outputs for some arguments.

The functions above will not run if z$=0$ due to a runtime error.