All Boolean Laws?

Question

Boolean Laws For Boolean Mathematics

1. Annulment

   A + 1 = 1

   A . 0 = 0

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2. Identity

   A + 0 = A

   A . 1 = A

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3. Idempotent

   A + A = A

   A . A = A

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4. Double Negation

   A̅̅ = A

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5. Complement

   A + A̅ = 1

   A . A̅ = 0

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6. Commutative

   A + B = B + A

   A . B = B . A

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7. De Morgon's Theory

   A̅+̅B̅ = A̅ + B̅

   A̅ .̅B̅ = A̅ + B̅

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8. Distributive

   A (B + C) = AB + AC

   A + (B . C) = (A + B) (A + C)

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9. Absorptive

   A + (A. B) = A

   A (A + B) = A

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10. Associative

    A + B + C = (A + B) + C = A + B + C

    A . B . C = (A . B) . C = A . B . C

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This is unknown law i found in here. (If this law has name pleas be kind and teach me.

1. Unknown 1

   A + A̅ B = A + B

   A . (A̅ +B) = A . B

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My Question : are these all Boolean laws that i would learn to solve Boolean mathematics? or there are another Boolean Laws that i missed? If there have please teach me.

Answer 1

The name of your unknown law is called as Redundant Literal Rule. For more information, I hope this site will help you. Hope it helps.

Answer 2

Those are the basic laws and theorems of boolean algebra. If you are solving for a test, I'd stick with those.

Redundancy and Consensus are offshoots from other Laws.

Redundancy has two forms. $$(X + \overline Y) • (X + Y) = X $$ $$X \overline Y + X Y = X$$

This is the form, you list:

$$(X + \overline Y) • Y = XY $$ $$X \overline Y + Y = X + Y$$

Consensus

$$(X + Y) • (\overline X + Z) • (Y + Z) = (X + Y) • (\overline X + Z)$$ $$X Y + \overline X Z + Y Z = X Y + \overline X Z$$

If you expand the terms, the last is absorbed into the first.

Laws and Theorems of Boolean Algebra