Quick Question about Conditional Statements

dazedandconfused-1

Hi all,

I had a few quick questions about conditional statements.

Say we have A --> B.

1) I know that if A is not met (sufficient) or B is met (necessary), I know that the conditional statement falls away (without needing to know the outcome of the other). But does falling away mean that the conditional statement is INVALID or that it is NOT TRUE (hence, false)?

2) Given A --> B, I know that the conditional statement is false if A is met but B is not met. But are there other ways for the conditional statement to be false other than the situation I've given above?

Thank you!

taschasp

1) No -- if the sufficient condition is not met, or if the necessary condition is met, in both of those cases it doesn't affect the conditional statement. The statement doesn't become invalid; it just becomes irrelevant.

Like, if I tell you that all the apples in my fridge are rotten (apple -> rotten). So you open the fridge and you see a pear. I didn't tell you anything about any non-apple things in my fridge, so my statement about apples is useless to you.

Similarly, based on the same conditional, if your friend came and pulled something out and told you it was rotten, you don't know if it was an apple or not, so the conditional statement isn't helpful there either. It could be an apple that's rotten, but it could also be something else that's gone bad, since I didn't tell you about whether apples were the only thing in my fridge that is rotten (if I did, that would have been rotten -> apple)

2) That's it. If I told you that all apples in my fridge are rotten (apple -> rotten) and you open my fridge and find an apple that isn't rotten, then you've proved my conditional statement to be false. You always do this by showing that you can meet the sufficient condition while denying the necessary condition -- in effect, it shows that the necessary condition (being rotten, in this case) wasn't necessary (for apples) after all! And it also shows that the sufficient condition (being an apple) wasn't sufficient (to be rotten).

dazedandconfused-1

thank you for your help!

taschasp

@"dazedandconfused-1" said:
thank you for your help!

Always glad to help, and I love the username--so fitting for the LSAT isn't it? I'm going on a Zeppelin listening spree now, it's been a while.