"If-Then" Tables Explained
Sans Doute
(Part 5)

So far we've filled in three rows of the "If-Then" Truth Table.

Truth Table: If-Then Statements
QH	RC	QH → RC
TRUE	TRUE	TRUE
TRUE	FALSE	?
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

And now let's pick another card.

And we get something weird:

Yep. We've picked the Queen of Hearts - but it's a black card.

And now what do we do?

Well, we did select the Queen of Hearts. So the antecedent is TRUE.

QH ≡ TRUE

But it's a black card. So in this case, the consequent is FALSE.

RC ≡ FALSE

So our entire statement:

QH → RC

... has the assignment:

TRUE → FALSE

Now that I've picked the right card but of the wrong color, is my original statement:

QH → RC

... TRUE or FALSE?

Clearly it's FALSE. I had said, IF I select the Queen of Hearts THEN it will be red. But the card was black. In other words, I fulfilled the required condition, but the outcome was not what I said it would be. So the entire statement is FALSE.

So we can now fill in the last incomplete row. And we get the final Truth Table:

Truth Table: If-Then Statements

QH	RC	QH → RC
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

Now to some this type of argument is convincing. But to others, it's still a bit iffy. There is, though, another way to show that this Table - as the commercials say - really, really works. Which you can finally see, if you click here.