Boundedness Law
X + 1 = 1
X . 0 = 0
 Â  
X + (X . Y) = X Elimination Law Associative Properties X + (Y + Z) = (X + Y) + Z
(X.Y'+Z).(X+Y).Z = X.Z+Y.Z instead of X.Z+Y'.Z
(X.Y'+X+Y).Z
Given a pair of terms for which a variable appears in one term, and its complement in the other, then the consensus term is formed by ANDing the original terms together, leaving out the selected variable and its complement. Example The consensus of X.Y and X'.Z is Y.Z The consensus of X.Y.Z and Y'.Z'.W' is (X.Z).(Z.W') Shannon Expansion Theorem
F = X . F (X = 1) + X' . F (X = 0)
= X . (Y . Z') + X' . (Y + Y' . Z) This is known as the cofactor of F with respect to X in the previous logic equation. The cofactor of F with respect to X may also be represented as F X (the cofactor of F with respect to X' is F X' ). Using the Shannon Expansion Theorem, a Boolean function may be expanded with respect to any of its variables. For example, if we expand F with respect to Y instead of X, Summary of Laws And Theorms

Boundedness Law
X + 1 = 1
X . 0 = 0
 Â  
X + (X . Y) = X Elimination Law Associative Properties X + (Y + Z) = (X + Y) + Z
(X.Y'+Z).(X+Y).Z = X.Z+Y.Z instead of X.Z+Y'.Z
(X.Y'+X+Y).Z
Given a pair of terms for which a variable appears in one term, and its complement in the other, then the consensus term is formed by ANDing the original terms together, leaving out the selected variable and its complement. Example The consensus of X.Y and X'.Z is Y.Z The consensus of X.Y.Z and Y'.Z'.W' is (X.Z).(Z.W') Shannon Expansion Theorem
F = X . F (X = 1) + X' . F (X = 0)
= X . (Y . Z') + X' . (Y + Y' . Z) This is known as the cofactor of F with respect to X in the previous logic equation. The cofactor of F with respect to X may also be represented as F X (the cofactor of F with respect to X' is F X' ). Using the Shannon Expansion Theorem, a Boolean function may be expanded with respect to any of its variables. For example, if we expand F with respect to Y instead of X, Summary of Laws And Theorms

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