Q$\mathrm{.}1$Set. $($A$)$ Simplify the following original equations and implement in ladder logic. Write down the assumptions and then logic for the implementation. A$+(/$bar $($B$)(+)/($b$)$ar $($C$)(+)/($b$)$ar $($D$))($B$(+)/($b$)$ar $($C$))+$A$*$B$*(/$bar $($C$)(+)/($b$)$ar $($D$))$ Q$\mathrm{.}1$Set. $($B$)$ Given the equation, A$()/($b$)=$ar $($B$)*(/$bar $($C$*((/$bar $($D$))+$E$+(/$bar $($C$))))(+)/($b$)$ar $($F$)*$C$).$ Implement the equation in digital logic and ladder diagram. Write down the assumptions and then logic for the implementation. $[6]$ Q$\mathrm{.}1$Set. $($C$)$ Draw a ladder diagram that is equivalent to the digital logic diagram in fig. $26$ Q$.1$ c