$1.$ The figure below shows a fault tree structure.

a$.$ Create the Boolean expression for the fault tree.

b$.$ Based on the Boolean expression, calculate the probability $($Hint: solve each contributor from the bottom prior to advancing upwards$).$

c$.$ Determine the minimal cut sets using method in presentation; calculate the probability and the importance of each cut set.

d$.$ Using Boolean algebra, further reduce the minimal cut sets and compare your answers with Part A$.$

e$.$ Critique the fault tree construction below based on the rules and general arrangement.