Logic 911 If Then Statements - HELP

[Blossom'sGirl]

Logic has never been my "thing" so I thought I would look over ds's Orbiting Logic problem for tomorrow and I am kinda stumped on the If False then False is True. For example:

 

 

If lions fly, then cows crow. LF- False CC- False LF -> CC True (huh?)

 

The book said that the only time an if /then statement is false is when the if statement is true and the then is false. I faintly understand this but I am not sure how I explain to false/ false statements to be true.

[forty-two]

Yeah, that's always a fun one :D. (And one of the standard examples trotted out by traditional logic types as to why symbolic logic is simply not as good for training kids to think.)

 

Ok, basically what "If A, then B" is saying is that A is a sufficient condition for B. IOW, the statement is saying that whenever A is true, you know that B is also true. So it is only false if A is true and B is false. If A is false, we don't care about B.

 

Here's an example of if A, then B to help explain:

 

Let's have

A = your dh said there was chocolate in the cabinet, and

B = whether there is chocolate in the cabinet.

 

You will only be mad if A is true - you were told there was chocolate - and B is false - there is no chocolate. Where they are both false - your dh didn't tell you there was chocolate and there was no chocolate - nothing was promised, so the fact that nothing was delivered isn't a problem.

 

Edited to add: In the other cases - you were told there was chocolate and there is chocolate (A=T,B=T), and you weren't told there was chocolate and there is chocolate (A=F,B=T) - everything is likewise fine, as you weren't lied to (if A, then B = T).

 

Does that help?

Edited January 6, 2010 by forty-two

[Blossom'sGirl]

Yes! Chocolate in the cupboard makes so much more sense than flying lions and crowing cows.

 

Thanks.