The conjunction of two propositions P and Q is the proposition that is true when the propositions P and Q are both true, and false if one of the two propositions is false.

### Symbol

The logical conjunction of the propositions P and Q is noted as “P ∧ Q” and is read as: “P or Q”.

### Properties

- The truth table of the conjunction is:

P |
Q |
P ∧ Q |

1 | 1 | 1 |

1 | 0 | 0 |

0 | 1 | 0 |

0 | 0 | 0 |

In which 1 = true and 0 = false.

- Logical conjunctions and logical disjunctions are connected by the De Morgan’s laws.

\(

\neg (P ∧ Q) ⇔ \neg P ∨ \neg Q \\

\neg (P ∨ Q) ⇔ \neg P ∧ \neg Q

\)