## Basic Laws of Boolean Algebra

##### Created by:

d_michel  on November 30, 2011

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# Basic Laws of Boolean Algebra

 CommutativeA || B = B || A A && B = B && A
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#### Definitions

Commutative A || B = B || A
A && B = B && A
Distributive A || (B && C) = (A || B) && (A || C)
A && (B || C) = (A && B) || (A && C)
Identity A || 0 = A
A && 1 = A
Inverse A || !A = 1
A && !A = 0
Idempotent A || A = A
A && A = A
Boundedness A || 1 = 1
A && 0 = 0
Absorption A || (A && B) = A
A && (A || B) = A
Associative A || (B || C) = (A || B) || C
A && (B && C) = (A && B) && C
Involution ! (!A) = A
Derived A || (!A && B) = A || B
A && (!A || B) = A && B
DeMorgan's! (A || B || C....) = !A && !B && !C &&....)
! (A && B && C &&....) = !A || !B || !C ||....

! (A || B) = !A && !B
The NOT of the Ors equals the AND of the NOTs.
"Since it is false that either thing is true, then both things must be false."
! (A && B) = !A || !B
The NOT of the ANDs equals the OR of the NOTs.
"Since it is false that two things together are true, at least one of them must be false."

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