Basic Laws of Boolean Algebra
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11 terms
Terms | 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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