Problem 4 120 points] BDDs Part 1 of 2 Consider the following three Boolean functions of three variables: P(a,b.c)-(a+bb+c(ac) la,b,c)- ab bc (a c) R(a,b,c)-ata'b+a'b'c (a) [10 points] Construct a single-rooted ROBDD for each of P. O and R using the same top-to-bottom variable ordering a, b, c in each case (b) [5 points Construct one multi-rooted ROBDD for all three functions P.Q. R c) [5 points] Give a short argument to show that the number of nodes cannot be reduced in any of your three ROBDDs for Part (a) by changing the variable order. Brute-force trial of all possible orders is not considered "short" Problem 4 120 points] BDDs Part 1 of 2 Consider the following three Boolean functions of three variables: P(a,b.c)-(a+bb+c(ac) la,b,c)- ab bc (a c) R(a,b,c)-ata'b+a'b'c (a) [10 points] Construct a single-rooted ROBDD for each of P. O and R using the same top-to-bottom variable ordering a, b, c in each case (b) [5 points Construct one multi-rooted ROBDD for all three functions P.Q. R c) [5 points] Give a short argument to show that the number of nodes cannot be reduced in any of your three ROBDDs for Part (a) by changing the variable order. Brute-force trial of all possible orders is not considered "short