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Boolean Algebra
Question
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State Distributive Laws of Boolean Algebra and verify them using truth table.

(i) X. (Y+Z)= X.Y + X.Z

(ii) X + Y.Z= (X + Y). (X+Z)

Answer

(i)

X Y Z Y+Z X.(Y+Z) X.Y X.Z X.Y+X.Z
0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0
0 1 0 1 0 0 0 0
0 1 1 1 0 0 0 0
1 0 0 0 0 0 0 0
1 0 1 1 1 0 1 1
1 1 0 1 1 1 0 1
1 1 1 1 1 1 1 1

(ii)
X Y Z Y.Z X+Y.Z (X+Y) (X+Z) (X+Y).(X+Z)
0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0
0 1 0 0 0 1 0 0
0 1 1 1 1 1 1 1
1 0 0 0 1 1 1 1
1 0 1 0 1 1 1 1
1 1 0 0 1 1 1 1
1 1 1 1 1 1 1 1

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