Why is the conclusion true when the hypothesis is false?

eg. If I am elected president, then i will bring world peace.





Then if the premise is false which is that I am not elected president, why is the conclusion true?





My tA said something that if i am not elected president, can you say I lied?





However, I think that you can't also say that he didn't too right? So how can you just say the conclusion is true when the premise is false?





Shouldn't the truth of the conclusion remained unknown rather then simply saying that it is true?





I am so confused.Why is the conclusion true when the hypothesis is false?
You have to say the truth in the conclusion.


In ex.


Through the number of trials in this experiment, I have concluded that the hypothesis is false, and I will not become the president.