Given the Fault Tree below,

a$.$ Determine the Minimum Path Sets. $($Show your work.$)$

b$.$ Construct the Reliability Block Diagram $($RBD$)$ for the Fault Tree

c$.$ Use Excel to construct the Truth Table and determine actual PT$.$ Use a light shade to distinguish those combinations that result in system failure $($i$.$e$.$ get you to the top$).$ Include your answer on the paper "hand$-$in$"$ portion as Homework $8$a$,$ and submit your spreadsheet through Canvas as Homework $8$b$.($For initiators $1-8,$ use $10\%$ as the failure probability.$)$

d$.$ Estimate PT based on Cut Sets $[$It will be helpful to you if you do this $($part d$)$ before you do part c$.]$