# Prove De-Morgan's Law Using Truth Table Answer With Hand Written Notes [Digital Electronics]

Prove De-Morgan's Law Using Truth Table Answer With Hand Written Notes [Digital Electronics], Digital Electronics ,Semester 2 , Kolhan University

**(2.) Prove De-Morgan's Law Using Truth Table. [KU - 2018]**

**ANS: De-Morgan's First Law : **

The first theorem of De Morgan's Law defines that the inverted result from AND Operation is the same as the OR operation of a complement of each variable where the Result equal NAND Operation.

__De-Morgan's First Law Formula____ __:

(X**•**Y)' = X' + Y'

__De-Morgan's First Law Truth Table__

X | Y | X' | Y' | X•Y | (X•Y)' | X'+Y' |
---|---|---|---|---|---|---|

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 |

__De-Morgan's Second Law__ :

The Second theorem of De Morgan's Law defines that the inverted result from OR Operation is the same as the AND operation of a complement of each variable where the Result equal NOR Operation.

__De-Morgan's Second Law Formula____ __:

(X**+**Y)' = X' • Y'

__De-Morgan's Second Law Truth Table__

X | Y | X' | Y' | X+Y | (X+Y)' | X'•Y' |
---|---|---|---|---|---|---|

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 |

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