Basic Theorem / Postulates of Boolean Algebra and its Truth Tables
1. Properties of 0 and 1
1.1.
0 + X = X
0
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X
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R
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0
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0
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0
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0
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1
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1
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1.2.
0.X = 0
0
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X
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R
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0
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0
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0
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0
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1
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0
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1.3.
1 + X = 1
1
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X
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R
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1
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0
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1
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1
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1
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1
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1.4.
1.X = X
1
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X
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R
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1
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0
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0
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1
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1
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1
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2. Idempotent Law
2.1.
X + X = X
X
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X
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R
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0
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0
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0
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1
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1
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1
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2.2.
X.X = X
X
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X
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R
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1
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0
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0
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1
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1
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1
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3.
Involution
3.1.
(X’)’ = X
X
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X’
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(X’)’
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0
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1
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0
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1
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0
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1
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4. Complement Law
4.1.
X + X’ = 1
X
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X’
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R
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0
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1
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1
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1
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0
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1
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4.2.
X.X’ = 0
X
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X’
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R
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0
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1
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0
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1
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0
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0
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5. Commutative Law
5.1.
X + Y = Y + X
X
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Y
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X+Y
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Y+X
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0
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0
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0
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0
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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5.2.
X.Y = Y.X
X
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Y
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X.Y
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Y.X
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0
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0
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0
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0
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0
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1
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0
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0
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1
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0
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0
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0
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1
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1
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1
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1
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6. Associative Law
6.1.
X + (Y + Z) = (X + Y) + Z
X
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Y
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Z
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X+Y
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Y+Z
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X+(Y+Z)
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(X+Y)+Z
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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0
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1
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1
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1
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0
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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0
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1
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0
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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6.2.
X.(Y.Z) = (X.Y).Z
X
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Y
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Z
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X.Y
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Y.Z
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X.(Y.Z)
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(X.Y).Z
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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0
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0
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0
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0
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0
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1
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0
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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1
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0
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0
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0
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0
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0
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0
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1
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0
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1
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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1
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1
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1
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1
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1
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1
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7. Distributive Law
7.1.
X(Y + Z) = XY + XZ
X
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Y
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Z
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Y+Z
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X.Y
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X.Z
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X.(Y+Z)
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X.Y+X.Z
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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1
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0
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0
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0
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0
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0
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1
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0
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1
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0
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0
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0
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0
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0
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1
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1
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1
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0
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0
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0
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0
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1
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0
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0
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0
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0
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0
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0
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0
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1
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0
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1
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1
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0
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1
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1
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1
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1
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1
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0
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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X
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Y
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Z
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Y.Z
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X+Y
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X+Z
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X+(Y.Z)
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(X+Y).(X+Z)
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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0
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0
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1
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0
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0
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0
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1
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0
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0
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1
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0
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0
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0
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0
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1
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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0
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1
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0
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1
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1
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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8 . Absorption Law
8.1.
X + XY = X
X
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Y
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X.Y
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X+(X.Y)
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0
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0
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0
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0
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0
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1
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0
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0
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1
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0
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0
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1
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1
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1
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1
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1
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8.2.
X .(X + Y) = X
X
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Y
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X+Y
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X.(X+Y)
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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1
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1
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1
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1
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1
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1
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9.
3rd Distributive Law
9.1.
X + X’Y = X + Y
X
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Y
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X’
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X’.Y
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X+ X’Y
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X+Y
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0
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0
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1
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0
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0
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0
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0
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1
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1
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1
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1
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1
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1
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0
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0
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0
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1
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1
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1
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1
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0
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0
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1
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1
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