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1.Simplify the following functions using ONLY Boolean Algebra Laws and Theorems. For each resulting simplified function,...

1.Simplify the following functions using ONLY Boolean Algebra Laws and Theorems. For each resulting simplified function, sketch the logic circuit using logic gates. (30points)

a.SimplifyF= (A+C+D)(B+C+D)(A+B+C) Hint:UseTheorem8 ,theorem 7 and distributive

̅̅b. Show that (Z + X)(Z +Y)(Y + X) = ? ? + ? ?

̅̅c. Show that (X +Y)Z + XYZ = ?.?

(15 points for simplification and 15 points for Logisim diagrams)

2. Prove the below equation using Boolean Algebra Theorems and laws Write the name of rules applied for each step ( 5 points)

(A+B)(A+B)B=(A+B)(A B+BB) = 0

3. Write any valid Boolean expression for Q as a function of the input variable

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