Sol_hw2[1]

# Sol_hw2[1] - Solution to Homework#2 Note In the following...

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Solution to Homework #2 Note: In the following solutions, the notation x' is equivalent to x . 2.1 (10 points) Proof: (x + y) • (x + z) = xx + xz + xy + yz = x + x z + x y + y z = x(1 + z + y) + yz = x 1 + y z = x + y z 2.2 (10 points) Proof: (x + y) • (x + y') = xx + xy + xy' + yy' = x + xy + xy' + 0 = x(1 + y + y’) = x 2.3 (10 points) Proof: xy + yz +x'z = xy + (x + x')yz + x'z = xy + xyz +x'yz +x'z = xy(1+z) + x'z(y+1) = x y + x ' z 2.4 (10 points) Proof using Venn diagrams:

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2.5 (10 points) Proof of 15a using Venn diagrams: x y x y x y x y x y x y x' (x y)' y' x' + y' (10 points) Proof of 15b using Venn diagrams: x y x y x y x y x y x + y x' (x + y)' y' x' y'
2.6 (10 points) Proof using Venn diagrams: x 1 + x 2 + x 3 x 1 x 2 x 3 x 1 x 2 x 3 x 1 x 2 x 3 x 1 x 2 x 3 x 1 + x 2 + x 3 ' (x 1 +x 2 +x 3 ) (x 1 +x 2 +x 3 ') x 1 + x 2 2.7 Note: Colors are used to help you understand the algebraic manipulation. Also, the manipulation process is not unique.

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## This note was uploaded on 01/31/2009 for the course ECEN 214 taught by Professor Su during the Fall '08 term at Texas A&M.

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Sol_hw2[1] - Solution to Homework#2 Note In the following...

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