I don't get the logical grid really
When they say "If A, then B"
They say if both are true, the IF-THEN is true - this I understand,
But I don't understand why and how
-- If A is false and B is true -- -- If A is false and B is false --
Don't they just make it neutral, i.e. doesn't it make it neither true nor false? Because in reality, if they say "If it rains, then I wear an umbrella", and it doesn't rain (A is false), how are we to prove that he would wear an umbrella if it DID rain, because we don't actually see it since it doesn't actually rain? Maybe I am getting too much into it (probably) but that part they say "this makes it true" is what I don't get. I believe it should be neutral, but I don't know for sure.
If anyone gets me and has an explanation, please.