$2$

DO NOT USE THE ABSORPTION LAW. USE ONLY SIMPLE BOOLEAN LAWS LIKE COMPLEMENT, IDENTITY, DISTRIBUTIVE, DEMORGANS, ETC.

$1$ point

Given the following Boolean function:

$F(W,x,Y,Z)=W^{\text{'}}{x}^{\text{'}}{Y}^{\text{'}}{Z}^{\text{'}}+W^{\text{'}}{x}^{\text{'}}Y{Z}^{\text{'}}+W{x}^{\text{'}}{Y}^{\text{'}}{Z}^{\text{'}}+W{x}^{\text{'}}{Y}^{\text{'}}Z+W{x}^{\text{'}}YZ+W{x}^{\text{'}}Y{Z}^{\text{'}}$

Prove that $F(W,x,Y,Z)=W{x}^{\text{'}}+x^{\text{'}}{Z}^{\text{'}}$ using Boolean algebraic minimization.

You must show all intermediate steps, stating the property, rule, or identity used to go from one step to the next.

For example:

$x(Y*0)=x(0)$ by short$-$circuit rule

$x(0)=0$ by short$-$circuit rule

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DO NOT USE THE ABSORPTION LAW. USE ONLY SIMPLE BOOLEAN LAWS LIKE COMPLEMENT, IDENTITY, DISTRIBUTIVE, DEMORGANS, ETC.