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B
OOLEAN
A
LGEBRA
OR
x
y
x + y
0
0
0
0
1
1
1
0
1
1
1
1
AND
x
y
x
·
y
0
0
0
0
1
0
1
0
0
1
1
1
Exclusive OR
x
y
x Å y
0
0
0
0
1
1
1
0
1
1
1
0
NOT
x
x
0
1
1
0
x + 0 = x
x
·
1 = x
x +
x
= 1
x
·
x
= 0
x + x = x
x
·
x = x
x + 1 = 1
x
·
0 = 0
Involution
Commutative
x + y = y + x
x
·
y = y
·
x
Associative
x + (y + z) = (x + y) + z
Distributive
x
·
(y + z) = x
·
y + x
·
z
x + y
·
z = (x + y)
·
(x + z)
DeMorgan
(x + y)
=
x
·
y
(x
·
y)
=
x
+
y
Absorption
x + x
·
y = x
x
·
(x + y) = x
