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Boolean Expression |
Description | Equivalent Switching Circuit |
Boolean Algebra Law or Rule |

A + 1 = 1 | A in parallel with closed = "CLOSED" |
Annulment | |

A + 0 = A | A in parallel with open = "A" |
Identity | |

A . 1 = A | A in series with closed = "A" |
Identity | |

A . 0 = 0 | A in series with open = "OPEN" |
Annulment | |

A + A = A | A in parallel with A = "A" |
Idempotent | |

A . A = A | A in series with A = "A" |
Idempotent | |

NOT A = A | NOT NOT A (double negative) = "A" |
Double Negation | |

A + A = 1 | A in parallel with NOT A = "CLOSED" |
Complement | |

A . A = 0 | A in series with NOT A = "OPEN" |
Complement | |

A+B = B+A | A in parallel with B = B in parallel with A |
Commutative | |

A.B = B.A | A in series with B = B in series with A |
Commutative | |

A+B = A.B | invert and replace OR with AND | de Morgan’s Theorem | |

A.B = A+B | invert and replace AND with OR | de Morgan’s Theorem |

Source : http://www.electronics-tutorials.ws/boolean/bool_6.html