URGENTLY $!!!!$

$-($a$)(5$ Points$)$ Design a half adder with a minimum number of $2-1$ multiplexers. The complements of the variables are NOT available. However, you can use logic $1$ and $0.$ No other gates are available.

$-($b$)(10$ Points$)$ Implement $\backslash (\backslash$mathrm$\{$F$\}(\backslash$mathrm$\{$X$\},\backslash$mathrm$\{$Y$\},\backslash$mathrm$\{$X$\})=\backslash$mathrm$\{$X$\}(\backslash$mathrm$\{$YZ$\}+\backslash$mathrm$\{$YZ$\})\backslash )$ with a single $2-$to$-4$ decoder and a single $2-$to$-1$ multiplexer.

$-($c$)(10$ Points$)$ Design a $3-$to$-8$ line decoder using two $2-$to$-4$ line decoders and eight $2-$input AND gates.