hi everyone!

I read a blog write about formula of a^b = a'b + ab' and i dont understand. Someone can explain it for me pls :((

(sorry i'm poor E).

link: https://www.homeworklib.com/qaa/1383353/2prove-that-a-xor-b-a-xor-c-a-xor-b-b-xor

# | User | Rating |
---|---|---|

1 | tourist | 3947 |

2 | ecnerwala | 3654 |

3 | jiangly | 3627 |

4 | jqdai0815 | 3620 |

5 | orzdevinwang | 3612 |

6 | Benq | 3586 |

7 | Radewoosh | 3582 |

8 | Geothermal | 3569 |

8 | cnnfls_csy | 3569 |

10 | ksun48 | 3474 |

# | User | Contrib. |
---|---|---|

1 | awoo | 163 |

2 | maomao90 | 160 |

3 | adamant | 156 |

4 | atcoder_official | 154 |

5 | maroonrk | 153 |

6 | -is-this-fft- | 148 |

6 | SecondThread | 148 |

8 | Petr | 147 |

9 | nor | 145 |

10 | cry | 144 |

hi everyone!

I read a blog write about formula of a^b = a'b + ab' and i dont understand. Someone can explain it for me pls :((

(sorry i'm poor E).

link: https://www.homeworklib.com/qaa/1383353/2prove-that-a-xor-b-a-xor-c-a-xor-b-b-xor

↑

↓

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/04/2024 14:16:51 (l2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|

Auto comment: topic has been updated by _Bunny (previous revision, new revision, compare).lol, that whole blog is shit. (a xor b) + (a xor c) = (a xor b) + (b xor c) is not true. U got (a xor b) on both sides, so basically ur saying that (a xor c) = (b xor c) which doesn't make sense. Simplest example you can prove it yourself is a = 1, b = 0, c = 1

something something dunning kruger

ah yes, (x+y)^2 = x^2 + y^2

I can't lie: I was gonna make this exact comment a few days ago, but I saw your comment, so I didn't end up commenting myself. I was even gonna preface my comment with a snarky little phrase, as you have.

Thank God you made it before me so we all can laugh at you instead.

It's not wrong. it's just that the blog is in the context of boolean algebra, where, in fact, a^b = a'b + ab'. Here, ' symbol represents the negation of the boolean value of the variables.

In boolean algebra, a^b is true when

a is false and b trueORa is true and b is false, predicate that is represented witha' and bora and b'which is just written asa'b+ab'thanks u very much.

Also the definition of $$$+$$$ and $$$\times$$$ differs from our common one. In boolean algebra, “ $$$+$$$ ” basically means bitwise xor and “ $$$\times$$$ ” means bitwise and. One can verify that these operations forms a ring.