"If-Then" Tables Explained*Sans Doute*

(Part 2)

Let's look at the "If-Then" Truth Table again.

Truth Table: If-Then Statements | ||

A | B | A → B |

TRUE | TRUE | TRUE |

TRUE | FALSE | FALSE |

FALSE | TRUE | TRUE |

FALSE | FALSE | TRUE |

Now this is intended for * logical arguments*. That is, discussions that deal with

And they must be TRUE or FALSE even if we don't know the answer - at least , we don't know the answer * yet*.

OK, let's begin by clearing the Truth Table. And then we'll figure out how to fill it back in.

Truth Table: If-Then Statements | ||

A | B | A → B |

TRUE | TRUE | ? |

TRUE | FALSE | ? |

FALSE | TRUE | ? |

FALSE | FALSE | ? |

What we will do is see how the TRUTH VALUES of the "If" part - called the * antecedent* - and of the "Then" part - called the

Now, suppose I have a deck of cards. And I make the statement:

If I select the Queen of Hearts, then it will be a red card.

Which we can abbreviate as:

If QH then RC

... or

QH → RC

So my table is now:

Truth Table: If-Then Statements | ||

QH | RC | QH → RC |

TRUE | TRUE | ? |

TRUE | FALSE | ? |

FALSE | TRUE | ? |

FALSE | FALSE | ? |

Now I pick a card. But it is the Queen of Clubs.

And what are the Truth Values?

Well, we didn't select the Queen of Hearts. So the antecedent is FALSE.

QH ≡ FALSE

And the Queen of Clubs is a black card. So the consequent is FALSE as well.

RC ≡ FALSE

So our entire statement:

QH → RC

... has the assignment:

FALSE → FALSE

OK. I've picked the wrong card of the wrong color. But is my original statement:

QH → RC

... TRUE or FALSE?

Well, it's TRUE. Why? Because picking the wrong card of the wrong color does not change the fact that **IF*** I pick* the Queen of Hearts

So we can fill in the blank, and the FALSE → FALSE part of the Truth Table is:

Truth Table: If-Then Statements | ||

QH | RC | QH → RC |

TRUE | TRUE | ? |

TRUE | FALSE | ? |

FALSE | TRUE | ? |

FALSE | FALSE | TRUE |

So now we'll continue - that is, if you click here.