# Logical Operations

## Negation

Negation means the opposite of the original statement. If p is the statement, then the negation of p will be denoted by ~p and read as “It is not the case that p”. So if p is true then ~p will be false and vice versa.

Example – If the statement p is “New Delhi is in India”, then ~p will be “New Delhi is not in India”.

p | ~p |

T | F |

F | T |

## Conjunction

Conjunction means adding two statements. If p, q are two statements, then “p and q” is a compound statement then It will be denoted by p ∧ q and referred to as the conjunction of p and q.

The conjunction of p and q will be true only if p and q both are true otherwise p and q will be false.

p | q | p ∧ q |

T | T | T |

T | F | F |

F | T | F |

F | F | F |

## Disjunction

Disjunction means oring of two statements. If p, q are two statements, then “p and q” is a compound statement. It is denoted by p V q and referred to as the disjunction of p and q. The disjunction of p and q is true whenever at least one of the two statements is true and if both statements are false then it will be false.

p | q | p V q |

T | T | T |

T | F | T |

F | T | T |

F | F | F |

## Implication or If…then **(⟶)**

An implication of p ⟶ q is the proposition “if p, then q.” It is false if p is true and q is false. The rest cases are true.

p | q | p ⟶ q |

T | T | T |

T | F | F |

F | T | T |

F | F | F |

## If And Only If (↔)

p ↔ q is a bi conditional logical connective so if the p and q both are the same for example p and q both are true or p and q both are false then it will be true otherwise it will be false.

p | q | p ↔ q |

T | T | T |

T | F | F |

F | T | F |

F | F | T |