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Boolean Laws For Boolean Mathematics

  1. Annulment

    A + 1 = 1

    A . 0 = 0

  1. Identity

    A + 0 = A

    A . 1 = A

  1. Idempotent

    A + A = A

    A . A = A

  1. Double Negation

    A̅̅ = A

  1. Complement

    A + A̅ = 1

    A . A̅ = 0

  1. Commutative

    A + B = B + A

    A . B = B . A

  1. De Morgon's Theory

    A̅+̅B̅ = A̅ + B̅

    A̅ .̅B̅ = A̅ + B̅

  1. Distributive

    A (B + C) = AB + AC

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

  1. Absorptive

    A + (A. B) = A

    A (A + B) = A

  1. Associative

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

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

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

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.

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    For A.(A̅ +B) = A.B, you can use the multiplicative law and identity law. A.(A̅ +B) = A.A̅ + A.B = 0 + A.B = A.B. The second one does not have any law associated to it. – 2017-02-01

2 Answers 2

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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.

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    @BachiNirosh You can accept the answer if it helped you. – 2017-02-01
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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