Truth Table Help...

Question

I need to write a Truth Table for this equation and don't know where to start.

~ A v (B • C) / B ⊃ C // ~ A  

Answer 1

1. Start by listing our the individual letters:

A | B | C

2. Add each sentence to your table as a column to the right of the letters:

A | B | C | ~ A v (B • C) | B ⊃ C || ~A

3. List out every possible ordering of true and false for the sentence letters. I've provided a pattern below that is useful for capturing every possible ordering:

A | B | C | ~ A v (B • C) | B ⊃ C || ~A

T | T | T |

T | T | F |

T | F | T |

T | F | F |

F | T | T |

F | T | F |

F | F | T |

F | F | F |

4. Finally, calculate the truth-value for each of the sentences on each of the rows. For example, on the first row we treat all three of A, B, and C as true. So, ~ A v (B • C) is true, B ⊃ C is true, and ~A is false. So, put those values on the first row.

A | B | C | ~ A v (B • C) | B ⊃ C || ~A

T | T | T | T | T || F

T | T | F |

T | F | T |

T | F | F |

F | T | T |

F | T | F |

F | F | T |

F | F | F |