[12] You are given the circuit shown below. a. Show the truth table for this circuit (include columns for A,B,C,F. b. Show the Product of Sums (POS) expression c. Show the Sum of Products (SOP) expression d. Transform the SOP expression to the POS expression by manipulating it using the boolean identities in the Unit04 class slides. Show your work and indicate which identity you used at each step