Please complete this circuit where the truth table should look like this but it is not the x $=0$ y $=0$ and z $=1$ inputs should equal $1$ but it is zero in this case. All other input outputs are the same. make sure to show the newly corrected drawing to its entirety. Only use NOR and inverter gates for the solution!!

Truth table:

$```$

$|$ X $|$ Y $|$ Z $|$ F $|$

$|---|---|---|---|$

$|0|0|0|1|$

$|0|0|1|0|$

$|0|1|0|1|$

$|0|1|1|1|$

$|1|0|0|1|$

$|1|0|1|1|$

$|1|1|0|1|$

$|1|1|1|0|$

$```$

Expected Output:

And the second truth table with the correction mentioned $($where the output for x$=0,$ y$=0,$ z$=1$ is $1$ instead of $0)$:

$```$

$|$ X $|$ Y $|$ Z $|$ F $|$

$|---|---|---|---|$

$|0|0|0|1|$

$|0|0|1|1|$

$|0|1|0|1|$

$|0|1|1|1|$

$|1|0|0|1|$

$|1|0|1|1|$

$|1|1|0|1|$

$|1|1|1|0|$

$```$