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Boolean Algebra RulesA + 0 = A | A + 1 = 1 | A x 0 = 0 | A x 1 = A | A + A = A | A + A' = 1 | A x A = A | A x A' = 0 | A'' = A | A + A'B = A + B | A + AB = A(1+B) = A(1) = A | (A+B)(A+C) = A+BC | A + B = B + A | AB = BA | A+B+C = A+(B+C) | A(B+C) = AB+AC |
LawsCommunative Law | A x B = B x A | | A + B = B + A | Associative Law | A x (B x C) = (A x B) x C | | A + (B + C) = (A + B) +C | Distributive Law | A x (B + C) = A x B + A x C | | A + B x C = (A+B)(A+C) |
| | DeMorgan Rules(AB)' = A' + B' | (A+B)' = A'B' | Y' = A' x B x C | Y = (A' x B x C)' | Y = A x B' x C' | (A x B x C)' = A' + B' + C' | (A + B + C)' = A' x B' x C' |
TheoremsTheorem 1 | X + X · Y = X | Theorem 2 | X + X' · Y = X + Y | Theorem 3 | X · Y + X' · Z + Y · Z = X · Y + X' · Z | Theorem 4 | X(X + Y) = X | Theorem 5 | X(X' + Y) = X · Y | Theorem 6 | (X + Y)(X + Y') = X | Theorem 7 | (X + Y)(X' + Z) = X · Z + X' · Y | Theorem 8 | (X + Y)(X' + Z)(Y + Z) = (X + Y)(X' + Z) |
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