IF YOU COULD INCLUDE ALL STEPS PLEASE INCLUDE ALL STEPS WANT TO LEARN

$($HAND WRITTEN PREFERABLY$)$IF YOU COULD SLOVE QUUESTION$2$ FIRST then rest I WILL RATE FAST PLEASE REFER TO PICTURES FOR FUNCTIONS THE $\text{'}$ ARE BARS $2.$ Complement the function $F$ by finding $\text{'}$F where $F(X,Y,Z)=\text{'}X(Y+\text{'}Z)(X+Z).$

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$3.$Consider the Boolean function $F(X,Y,Z)=\text{'}$X$\text{'}$Y$+$Y$+\text{'}$XZ$.$

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a$.$ Write the function as a sum of minterms. Put your final answer here but show your work on your

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b$.$ Write the function as a product of maxterms. Put your final answer here.

c$.$ Draw a logic diagram for the original function on your calculations pages.

d$.$ Simplify the function using Boolean algebra. Put your final answer here.

$4.$ Optimize the following functions using a Karnaugh map. Put final answers below, but show K$-$map

work on calculations pages.

a$.F(X,Y,Z)=\text{'}$X$\text{'}$Z$+$Y$\text{'}$Z$+$XYZ Put your final answer here in SOP form.

b$.F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}m(0,1,4,5,6).$ Put your final answer here in SOP form. WILL RATE FAST PLEASE DO IT HANDWRITTEN IF YOU CAN!!!!! DO ALL IF YOU CAN PLEASE