I previously posted a logic rules cheat sheet and figured it was about time that I do the same for boolean algebra.

Expression | Equivalent To | Name of the Rule |
---|---|---|

$$ X + Y $$ | $$ Y + X $$ | Commutative |

$$ X \cdot Y $$ | $$ Y \cdot X $$ | Commutative |

$$ (X + Y) + Z $$ | $$ X + (Y + Z) $$ | Associative |

$$ (X \cdot Y) \cdot Z $$ | $$ X \cdot (y \cdot Z) $$ | Associative |

$$ X + (Y \cdot Z) $$ | $$ (X + Y) \cdot (Z + Z) $$ | Distributive |

$$ X \cdot (Y + Z) $$ | $$ (X \cdot Y) + (X \cdot Z) $$ | Distributive |

$$ X + 0 $$ | $$ X $$ | Identity |

$$ X \cdot 1 $$ | $$ X $$ | Identity |

$$ X + X' $$ | $$ 1 $$ | Complement |

$$ X \cdot X' $$ | $$ 0 $$ | Complement |

$$ X + X $$ | $$ X $$ | Idempotence |

$$ X \cdot X $$ | $$ X $$ | Idempotence |