I have just started studying mathematical reasoning and have come through one simple foolish problem.
I have learn that if '$\vee$' is used as connective and if any one component statement is true than compound statement is also true and if all the component statments are false then compound statement is false.
But is it possible that even though all the component statements are false, the compound statement is true?
NOTE= i have just started studying mathematical reasoning, so i don't to to much about it.
Each time you introduce a connective, you get to decide when you want it to be true and when you want it to be false. We introduce the connective $\vee$ and call it "or". Now, "or" is an English word. So, it would be best if the connective $\vee$ had a truth table that agrees with the English word. In English if I say "$A$ or $B$ is true" then I would be lying if both $A$ and $B$ are false. You could certainly define other connectives that are true when both pieces are false. It just wouldn't be good to use a word from English that doesn't fit with the situation.