### Day 43: Boolean Algebra

Hello Dear Students,

Hope you all are doing good...

So, aaj hum boolean algebra topic ko cover karenge,

Let's get started...

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__BOOLEAN ALGEBRA__- Boolean Algebra was first developed by George Boole in 1854, but the formal definition was given by E.V.Huntington in 1904.
- Boolean ka matlab hota hai true or false, here 0 and 1.
- Boolean Algebra is a branch of mathematics algebra.
- Boolean algebra is set of 3 operations which are-

**+ (similar to logical OR), also denoted as ∨****・(similar to logical AND), also denoted as ∧****ー (NOT), also denoted as prefix ᄀ**

- There are only 2 values i.e. 0 and 1, agar hum koi bhi operation perform karenge so uska result 0 and 1 mein hi ayega, whether 0, 1, or combination of 0 and 1.

The Truth Table of these 3 operations, AND, OR, NOT as as follows-

**Truth Table for AND**

A | B | R |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

**Truth Table for OR**

A | B | R |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

**Truth Table for NOT**

A | R |

0 | 1 |

1 | 0 |

**PRECEDENCE OF BOOLEAN OPERATIONS**

Operator | Symbol | Precedence |

Parenthesis | ( ) | First Priority for solving Parenthesis |

AND | ・ | Highest |

OR | + | Middle |

NOT | ー | Lowest |

- Duality Principle - Duality principle is very simple. In this, replace 0 with 1 and 1 with 0. And also replace + with ・, and ・ with +.
- Note that, because boolean algebra has only 2 values, 0 and 1, then the complement of 1 is 0, and the complement of 0 is 1.

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