Write a Boolean equation in sum$-$of$-$product form for the following truth tables. Minimize each equation using Boolean algebra $($where applicable, for each step, label the axiom or theorem used via given notes$).a,b,c,d$ are the inputs, and $y$ is the output. Draw the logic diagram implementing each minimized equation.

i$.)$

$\backslash$table$[[a,b,y$