Why is it that when A is false and B is false, we infer that A->B is true?
If A isn't true then we don't know if maybe when it is true then B would be false. could be B would be true, could be it'd be false.
Let's say A=it's raining B=worms come out
If A is false i.e. it's not raining.. and B is false, worms don't come out.. That shouldn't mean that A->B is true. Maybe when it is raining, worms won't come out.
Surely A->B shouldn't be true when A and B are false, it'd just be that you can't prove it to be false.You can only know it's false when you know the A is true and B is false case. But if A is false, you don't know what will happen when A is true.
The only two cases of the truth table that make sense to me as A=true B=true A->B=true . As then you know for sure A->B. Or A=true B=false A->B false, because then you know for sure A->B is false. But if A isn't happening, i.e. if A is false, then how can you judge A->B?
When we say A=true, do we mean A is always true? Or do we mean If/When A=true?
See if you say = true/false means always e.g. A= false, and you say that means A is always false... then I don't see how you could get A=false B=false A->B true. The two could have no connection and never be true.
like, let's say we us an example where A is always false and B is always false. If the clouds drop to the ground, then pigs will fly. I can't prove it true by showing that A=true B=true. I can't prove it false by showing A=true B=false.
and if we take a different example, one where B is always true.. A=I jump B=The Sun Shines. If I jump then the sun shines. Then I can accept the two easy ones that I can always accept A=true B=true A->B=true. I can accept the meaning of A=true B=false A->B=false, and it doesn't apply as B=true. Of the two difficult cases.. I can accept A=false B=true A->B=true because I can reason that the rule is saying that If A happens then B happens and even if A doesn't happen then B happens. So , if B happens, regardless of whether A caused it or not(i'm sure that's wrong there). But anyhow either way, I can't then understand that rule of A=false B=false A->B=true
If a teacher, knowing a student will fail a test, could say "If you pass that test, i'll eat my hat", then the teacher is safe, he won't have to eat the hat. The teacher won't be proven wrong.. but he's not really proven right either. As a promise it can potentially be true, but one would never really know if it's true.