Parts $($a$),($b$),$ and $($c$)$ refer to the following Boolean expression:

F$($X$,$ Y$,$ Z$)=$ XZ $+$ XYZ$+$Y$$Z $+$ XZ

$(10$ points$)$ Create a truth table for the expression.

$(10$ points$)$ Simplify the expression using a Karnaugh map.

$(10$ points$)$ Draw the two$-$level logic diagram for the simplified expression using only NAND gates and inverters. Assume that the complements of the inputs are not available.