ECE 275 Boolean Algebra
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AND Theorem
X * 0 = 0 X * 1 = X
OR Theorem
X + 0 = X X + 1 = 1
Idempotent Laws
X + X = X X * X = X
Laws of Complementarity
X + X' = 1 X * X' = 0
Elimination Theorem
X + X'Y = X + Y X(X' + Y) = XY
Absorption Theorem
X + XY = X X(X + Y) = X
Commutative Laws
X + Y = Y + X XY = YX
Distributive Laws
X(Y+Z) = XY + XZ X + YZ = (X + Y)(X + Z)
Consensus Theorem
XY + X'Z + YZ = XY + X'Y (X + Y)(X' + Z)(Y + Z) = (X + Y)(X' + Z)
Uniting Theorem
XY + XY' + X (X + Y)(X + Y') = X
Associative Law
(X + Y) + Z = X + (Y + Z) = X + Y + Z (XY)Z = X(YZ) = XYZ
DeMorgan Law
(X + Y)' = X'Y' (XY)' = X' + Y'
Involuntion Law
(X')' = X
