Using Boolean theorems and laws show that the Boolean function (XY.Z) = (X+Y)(X\

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Using Boolean theorems and laws show that the Boolean function (XY.Z) = (X+Y)(X'+Z)Z'Y' - X(Y+Z) + (ZYX-YXZYX+XZ) can be simplified toX(Y-Z). (b) Prove equality of the above two Boolean expressions using a truth table. (c) Show mat the simplification process in part (a) has significantly reduced the number of logic gates required to implement the expression Include the following in your answer: Draw the two networks (network for the original expression and network for the reduced expression) using only 2-input AND and OR gates. Assume mat you can use complemented (inverted) variables as inputs to your networks. You should not attempt to simplify the expressions, but you should reuse gates, if possible. The diagrams must be near enough for the marker to understand and grade them. Mention how many gates have been "saved" by this simplification

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