**E.g.1**

De Morgan's laws are indispensable in digital electronics. The laws outlined by him are simple to understand, yet transformed the Boolean algebra in a dramatic way.

**A + B = A.B**

**Proof:**

Input and Output | |||
---|---|---|---|

A | B | A+B | A + B |

1 | 0 | 1 | 0 |

0 | 1 | 1 | 0 |

0 | 0 | 0 | 1 |

1 | 1 | 1 | 0 |

Input and Output | ||||
---|---|---|---|---|

A | B | A | B | A.B |

1 | 0 | 0 | 1 | 0 |

0 | 1 | 1 | 0 | 0 |

0 | 0 | 1 | 1 | 1 |

1 | 1 | 0 | 0 | 0 |

**A.B = A + B**

**Proof:**

Input and Output | |||

A | B | A.B | A.B |

1 | 0 | 0 | 1 |

0 | 1 | 0 | 1 |

0 | 0 | 0 | 1 |

1 | 1 | 1 | 0 |

Input and Output | ||||

A | B | A | B | A + B |

1 | 0 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 |

0 | 0 | 1 | 1 | 1 |

1 | 1 | 0 | 0 | 0 |

Now try the following with a circuit and a truth table:

- A + B.C = A.B.C
- A + B.C + A.B = A.B
- A + AB = A + B
- AB + AB = A

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