# Prove the logical equivalence of the following statements, ~(p V ~q) V (~p ^ ~q) ≡ ~p

## Solution for ~(p V ~q) V (~p ^ ~q) ≡ ~p

~(p V ~q) V (~p ^ ~q) ≡ ~p | ||

1 | (~p ^ ~(~q)) V (~p ^ ~q) | (De Morgan’s law) |

2 | (~p ^ q) V (~p ^ ~q) | (Double negative law) |

3 | ~p ^ (q V ~q) | (Distributive law) |

4 | ~p ^ t | (Negation law) |

5 | ~p | (Identity law) |

Hence proved.