# DeMorgan’s Theorem

**DeMorgan’s Theorem:**

**Theorem 1:**

Statement: “The complement of two or more variable ANDed is equivalent to the OR of the Complements of the individual variables.

**(XY)’ = X’ + Y’**

X | Y | (XY)’ | X’+Y’ |

0 | 0 | 1 | 1 |

0 | 1 | 1 | 1 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 0 |

**Explanation**:

According to this theorem the result of the first NAND gate is equivalent to the result of the second Negative-OR gate when the X and Y is reversed and passed to the Negative-OR gate.

**Theorem 2**

Statement: “The complement of two or more variables ORed is equivalent to the AND of the complements of the individual variables”.

**(X+Y)’=X’Y’**

X | Y | (X+Y)’ | X’Y’ |

0 | 0 | 1 | 1 |

0 | 1 | 0 | 0 |

1 | 0 | 0 | 0 |

1 | 1 | 0 | 0 |

Explanation:

According to this theorem the result of the first NOR gate is equivalent to the result of the second Negative-AND gate when the X and Y is reversed and passed to the Negative-AND gate.