## Laws Of Boolean Algebra

The Laws Of Boolean Algebra is provided here.

#### OR

A + 0 = A

A + A’ = 1

A + B = B + A

A (B + C) = AB + AC

A + A = A

A + 1 = 1

A + AB = A

A + (B + C) = (A + B) + C

A” = A

#### AND

A . 1 = A

A . A’ = 0

A . B = BA

A + BC = (A + B) (A + C)

A . A = A

A . 0 = 0

A (A + B) = A , ( AA+ AB = A, A + AB = A)

A (BC) = (AB) C

## Distributive Law:

A . (B + C) = (A . B) + (A . C)

A + (B . C) = (A + B) . (A + C)

## Associative Law:

A + (B + C) = (A + B) + C

A . (B .C) = (A . B) . C

## Demorgan’s Theorem:

1. (AB)’ = A’ + B’

The product of the compliment is equal to the sum of the compliments

### Proof:

A | B | A’ | B’ | (AB) | (AB)’ | A’ + B’ |

0 | 0 | 1 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 0 | 1 | 1 |

1 | 0 | 0 | 1 | 0 | 1 | 1 |

1 | 1 | 0 | 0 | 1 | 0 | 0 |

2.(A + B)’ = A’ . B’

The sum of the compliment is equal to the product of the compliments.

### Proof:

A | B | A’ | B’ | (A + B) | (A + B)’ | A’. B’ |

0 | 0 | 1 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 | 0 | 0 |

1 | 0 | 0 | 1 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 1 | 0 | 0 |