# Cheatsheet Logic

## Boolean operators

"negation" (not \( a \)):

\( a \) | \( \lnot a \) |
---|---|

0 | 1 |

1 | 0 |

"and" also known as "conjunction" (\( a \) and \( b \)):

\( a \) | \( b \) | \( a \land b \) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

"inclusive or" also known as "disjunction" (\( a \) or \( b \)):

\( a \) | \( b \) | \( a \lor b \) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

"exclusive or" (\( a \) xor \( b \)):

\( a \) | \( b \) | \( a \oplus b \) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

"implication" (if \( a \), then \( b \)):

\( a \) | \( b \) | \( a \Rightarrow b \) |
---|---|---|

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 0 |

1 | 1 | 1 |

"iff" also known as "bi-implication" (if and only if \( a \), then \( b \))

\( a \) | \( b \) | \( a \Leftrightarrow b \) |
---|---|---|

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

## Derivation Rules

negation