(a) Determine an un-simplified logic R function for the output of the logic network shown here. Then, simplify the logic function as much as possible using Boolean Algebra. (b) Draw a logic network corresponding with the logic function F(W, X, Y, Z) shown below. F(W, X, Y, Z) = (WX' + Y)(XYZ' + (W + Z)) Assume the inputs of F(W, X, Y, Z) are only available in true form. (c) Use truth tables to prove the validity of the following Boolean equations. i. (A + C)(AB + C') = AB + AC', ii. W'XY + WZ = (W' + Z)(W + XY) (d) Simplify each of the following using the true or dual form of the Consensus Theorem i. BC'D' + ABC' + AC'D + AB'D + A'BD' (reduces to three terms) ii. (B + C + D)(A + B + C)(A' + C + D)(B' + C + D') (reduces to three terms) (e) Reduce the following Boolean logic expressions to minimum SOP form: i. (X + W)(Y Z) + XW' (reduces to three terms) ii. (A BC) + BD + ACD (reduces to four terms) (f) Consider each of the following logic functions shown below. f(A, B, C, D) = (A + BC)(AD + B(C + A)) f(A, B, C, D) = ABC + (A + B + D)(ABD + B) i. Compute the compliment of each logic function. Simplify each complemented function until every literal appears in either true or complement form. ii. Compute the dual of each logic function