Logic Symbols are part of a modern logical system for expressing rational thought and common patterns of reasoning. These symbols are used to clearly represent often times highly complex logical relationships between statements. There are five special symbols that are employed as statement connectives or operators; these are the logical symbols. The five logical symbols are all truth-functional connectives and will be discussed in more detail below. The symbols are ~ (also symbolized as �), & (also symbolized as or ^), v, (also symbolized as ⊃), and <-> (also symbolized as ). Logical symbols are used in a language that has several parts. Propositions are the statements that can be either true or false. These individual statements are usually represented by capital letters of the alphabet and are called statement constants. They are normal declarative sentences but are represented by statement constants for convenience. The statement connectives are the logical symbols whose function is to form new compound statements. These connectives can be reapplied to the resulting compound statements to form new compounds of compounds.

Symbol |
Symbol Name |
Meaning/Definition |
Example |

1) ⋅ | And | And | a ⋅ b |

2) ^ | Caret/Circumflex | And | a ^ b |

3) & | Ampersand | And | p & q |

4) + | Plus | Or | o + m |

5) ⋁ | Reversed caret | Or | p ⋁ q |

6) ∣ | Vertical line | Or | x ∣ y |

7) ' | Single quote | Not negation | p' |

8) ^{ - } |
Bar | Not negation | p^{-} |

9) ¬ | Not | Not negation | ¬ o |

10) ! | Exclamation mark | Not negation | !x |

11) ⊕ | Circled plus/ oplus | Exclusive or - xor | p ⊕ r |

12) ˜ | Tilde | Negation | ˜x |

13) ⇒ | Implies | ||

14) ⇔ | If and only if | ||

15) ∀ | For all | ||

16) ∃ | There exists | ||

17) ∄ | There does not exists | ||

18) ∴ | Therefore | ||

19) ∵ | Because/ Since |

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