Boolean Identities
Boolean Identities and Simplification
For each of the following Boolean Identities use a truth table and LogiSim or https://logic.ly/demo/to VERIFY that the Identity is true… This might seem like a really long winded task but it is essential that you REALLY believe and are comfortable with this form of algebra. ¬ = NOT, x = AND, + = OR
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Name |
Axiom |
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Idempotent |
A + A = A |
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Identity |
A + 0 = A A + 1 = 1 |
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Complement |
A + ¬A = 1 ¬(¬A) = A |
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Commutative |
A + B = B + A |
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Associative |
(A + B) + C = A + (B + C) |
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Distributive |
A × (B + C) = A × B + A × C |
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Absorption |
A + A × B = A A + ¬A × B = A + B |
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De Morgan’s |
¬(A + B) = ¬ A × ¬ B |
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