A combinational circuit has three inputs $($A$,$B$,$C$)$ and five outputs $($V$,$W$,$X$,$Y$,$Z$).$ VWXYZ represents a $2-$out$-$of$-5$ coded number whose value equals the number of $0\text{'}$s at the input. For example, if ABC $=110,$ VWXYZ $=00101.($a$)$ Complete the truth table. $($b$)$ Find the minterm expansion for X and Y$.($c$)$ Find the maxterm expansion for V and Z$.$