Consider the following:
I have promised George that if I find $10.00 on the ground then I will treat him to a movie.
Under the following cases:
- I find $10.00 then take George to a movie. I have not lied. Therefore the statement is true.
- I find $10.00 then don't take George to a movie. I have lied. Therefore the statement is false.
- I do not find $10.00 then take George to a movie. I have not lied. Therefore, the statement is true.
- I do not find $10.00 then don't take George to a movie. I have not lied. Therefore the statement is true.
So, the "truth table" for an if statement evaluated as a whole is as follows:
"(If A then B) = Result (or R)"
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| A | B | R |
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| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
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T = True; F = False
This is a useful way of determining if one variable is dependant on another. In the above scenario, the two events are independent. When the two variables are dependant (B is directly based on the state of A) the "if truth table" looks like this:
"If (A) then B"
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| A | B |
---------
| T | T |
| F | F |
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T = True; F = False