1. (10 pts each) Use the Boolean Postulates and Theorems (table 2.2 of the textbook) to simplify the following expressions as far as possible. Show and justify each step by citing the theorem or postulate used. a. f(A,B,C,D) = ABC + AB + ABC + AC + ABC b. f(W.x.Y.z)-(W +Y+Z)(X+D(W +X +Z)(X +Y)(X+Y+z) f(A,B,C) = (A + B)(A + AB)(A + B + ABC) + (A + B)(A + C) 2. (10 pts each) Given each function shown, take its complement and then use DeMorgan's theorem to eliminate all group complements from your final expression (Taking the complement simply means to place a bar over the entire expression.) c. (A+BCXA+DE) 3. (5 pts each) Given the following logic circuit f(A, B. C, D) a. Write the Boolean equation for f(A,B,C,D) from the above diagram. b. Write the complete truth table for f(A,B,C,D). c. Find the minimum sum-of-products (SOP)expression for f(A,B.CD) Show your steps and justify your answer. d. Draw the logic circuit equivalent to the minimum SOP expression you found in part (c)