logic boolean algebra proofs

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13 Terms

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Identity
A1 = A or A + 0 = A
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Null Element
A0 = 0 or A + 1 = 1
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Idempotency
AA = A or A + A = A
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Involution or Double Negation
A'' = A
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Complements
AA' = 0 or A + A' = 1
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Commutativity
AB = BA or A + B = B + A
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Associativity

(AB)C = A(BC) or (A + B) + C = A + (B + C)

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Distributive
(AB) + (AC) = A (B + C)
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Distributive
(A + B)(A + C) = A + (BC)
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Absorption/Covering

A(A + B) = A or A + (AB) = A
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Combining
(AB) + (AB') = A or (A + B)(A + B') = A
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Consensus
(AB) + (A'C) + (BC) = AB + A'C or (A + B)(A' + C)(B + C) = (A + B) (A' + C)
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De Morgan
(AB)' = A' + B' or (A + B)' = A'B'