"If-Then" Tables Explained
Sans Doute
(Part 4)

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

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

We did this by showing that if we pick the wrong card of the right color or the wrong card of the wrong color, this doesn't change the truth of the original statement. If the antecedent is FALSE, the "If-Then" statement is TRUE.

And now let's pick the right card, the Queen of Hearts.

And now what are the Truth Values?

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

QH ≡ TRUE

And it IS is a red card. So in this case, the consequent is also TRUE.

RC ≡ TRUE

So our entire statement:

QH → RC

... has the assignment:

TRUE → TRUE

Since we've picked the right card of the right color, we again ask is our original statement:

QH → RC

... TRUE or FALSE?

Of course, it's TRUE. I said, IF I select the Queen of Hearts THEN it will be red. And that's what happened. So the statement is TRUE.

So we can now fill in the blank, for the TRUE → TRUE part of the Truth Table:

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

Now you see there's just one little thing to finish. And we'll do that if we click here.