Question 1 (20 pts.) Demonstrate the validity of the following identities by means of truth tables: 1. DeMorgan's theorem for three variables: (x + y +z)' = x'y'z' and (xyz)' = x+y+z' 2. The distributive law: x + yz=(x + y)(x + 2) 3. The distributive law: x(y + 2) = xy + xz 4. The associative law: x + (y + z) = (x + y) + z 5. The associative law and x(yz) = (xyz Question 2 (20 pts.) Reduce the following Boolean expressions to the indicated number of literals: (a) A'C' + ABC + AC' to three literals (b) (x'y' +z)' + 2 + xy + wz to three literals (c) A'B(D' + C'D) + B(A + A'CD) to one literal (d) (A' + C) (A' + C') (A + B + C'D) to four literals (e) ABCD + A'BD + ABCD to two literals Draw logic diagrams of the circuits that implement the original and simplified expressions