0,0 | 0,1 | 1,0 | 1,1 | (p,q) | |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | ⤫ | false |

0 | 0 | 0 | 1 | ⤭ | AND |

0 | 0 | 1 | 0 | ⤫ | https://en.wikipedia.org/wiki/Material_nonimplication |

0 | 0 | 1 | 1 | ⤫ | p |

0 | 1 | 0 | 0 | ⤫ | https://en.wikipedia.org/wiki/Converse_nonimplication |

0 | 1 | 0 | 1 | ⤫ | q |

0 | 1 | 1 | 0 | ⤭ | XOR, != |

0 | 1 | 1 | 1 | ⤭ | OR |

1 | 0 | 0 | 0 | ⤭ | NOR |

1 | 0 | 0 | 1 | ⤭ | XNOR, == |

1 | 0 | 1 | 0 | ⤫ | !q |

1 | 0 | 1 | 1 | ⤫ | https://en.wikipedia.org/wiki/Converse_implication |

1 | 1 | 0 | 0 | ⤫ | !p |

1 | 1 | 0 | 1 | ⤫ | https://en.wikipedia.org/wiki/Material_conditional |

1 | 1 | 1 | 0 | ⤭ | NAND |

1 | 1 | 1 | 1 | ⤭ | true |

- ⤫
- non-commutative
- ⤭
- commutative

Note: Based on https://en.wikipedia.org/wiki/Truth_table#Binary_operations BUT with reordering the rows of the first table for our sort order