# Logic symbols

**Logic symbols**:

In logic, a set of symbols is commonly used to express logical representation. As logicians are familiar with these symbols, they are not explained each time they are used.

Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|

· |
and | and | x · y |

^ | caret / circumflex | and | x ^ y |

& | ampersand | and | x & y |

+ | plus | or | x + y |

∨ | reversed caret | or | x ∨ y |

| | vertical line | or | x | y |

x‘ |
single quote | not – negation | x‘ |

x |
bar | not – negation | x |

¬ | not | not – negation | ¬ x |

! | exclamation mark | not – negation | ! x |

⊕ | circled plus / oplus | exclusive or – xor | x ⊕ y |

~ | tilde | negation | ~ x |

⇒ | implies | ||

⇔ | equivalent | if and only if (iff) | |

↔ | equivalent | if and only if (iff) | |

∀ | for all | ||

∃ | there exists | ||

∄ | there does not exists | ||

∴ | therefore | ||

∵ | because / since |

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