$($i$)$ Output $x$ will equal A when inputs $B$ and $C$ are different

$($ii$)$ Output $x$ will remain HIGH when $B$ and $C$ are the same.

c$)$ Set up a truth table for the following circuit for the $16$ possible

$4$

combinations of inputs A$,$ B$,$ C$,$ D$.$ Hence write down the sum$-$ofproducts expression for $Z$ and simplify using K$-$map.