Consider the following problem:

Four chairs A$,$ B$,$ C$,$ and D are placed in a row. Each chair may be occupied $("$l$")$ or empty

$("0").$ A Boolean function $F$ is $"l"$ if and only if there are two or more adjacent chairs that

are empty.

a$.$ Give the truth table defining the Boolean function $F.$

b$.$ Express $F$ as a minterm expansion $($standard sum of product$).$

c$.$ Express $F$ as a maxterm expansion $($standard product of sum$).$

d$.$ Using postulates and theorems of Boolean algebra, simplify the minterm expansion of $F$

to a form with as few occurrences of each as possible.