I am studying Daniel J. Velleman's How to Prove it. I am various truth tables.
The truth table for . These were simple to
understand with their comparison to usual English language equivalent. But I am having difficult time understanding the truth table of .
The author gives an example of
"If then ".
I can see why the statement is true when both P and Q is true. I can see the
truth of the statement when both and are true. But author then says that is true
even when and are both false. I have trouble following
his arguments. We don't think like that in ordinary world. Can people help me ?
Edit: I read on many web sites about the explanations but I didn't find it satisfactory. So I am
going to ask here.