PROBLEM 1 (27 PTS) a) Simplify the following functions using ONLY Boolean Algebra Theorems. For each resulting simplified function, sketch the logic circuit using AND, OR, XOR, and NOT gates. (14 pts) F=A(B + C) + A F(X,Y,Z)=11(M2,M,,M,, M,) v v b) Using ONLY Boolean Algebra Theorems, demonstrate that the XOR operation is associative: (5 pts) c) For the following Truth table with two outputs: (8 pts) " Provide the Boolean functions using the Canonical Sum of Products (SOP), and Product of Sums o o o oo 0 0 1 1 0 0 1 01 1 0 1 1 1 1 (POS) Express the Boolean functions using the minterms and maxterms representations Sketch the logic circuits as Canonical Sum of Products and Product of Sums 1 0 10 1 1 1 0 1 1 1 1 1 0 1