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# Mathematical Logical Connectives

A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.

Generally there are five connectives which are −

OR (∨)

AND (∧)

Negation/ NOT (¬)

Implication / if-then (→)

If and only if (⇔).

**OR (∨)** − The OR operation of two propositions A and B (written as A ∨ B) is true if at least any of the propositional variable A or B is true.

The truth table is as follows −

A | B | A ∨ B |
---|---|---|

True | True | True |

True | False | True |

False | True | True |

False | False | False |

**AND (∧)** − The AND operation of two propositions A and B (written as $A \land B$) is true if both the propositional variable A and B is true.

The truth table is as follows −

A | B | A ∧ B |
---|---|---|

True | True | True |

True | False | False |

False | True | False |

False | False | False |

**Negation (¬)** − The negation of a proposition A (written as ¬ A) is false when A is true and is true when A is false.

The truth table is as follows −

A | ¬ A |
---|---|

True | False |

False | True |

**Implication / if-then (→)** − An implication A → B is the proposition “if A, then B”. It is false if A is true and B is false. The rest cases are true.

The truth table is as follows −

A | B | A → B |
---|---|---|

True | True | True |

True | False | False |

False | True | True |

False | False | True |

**If and only if (⇔)** − A ⇔ B is bi-conditional logical connective which is true when p and q are same, i.e. both are false or both are true.

The truth table is as follows −

A | B | A ⇔ B |
---|---|---|

True | True | True |

True | False | False |

False | True | False |

False | False | True |

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