TITLE: Why a false statement can imply anything?
QUESTION [8 upvotes]: According to the truth table,
If $P$ is false,then $P->Q$ is true.
if pigs fly, then $1+1=3$. Why is this implication true? How do you prove it?

REPLY [5 votes]: We know "pigs can't fly" is true, and by the law of the excluded middle, only one of the statements of { "pigs can't fly" , "pigs can fly"} is true.
But if we now suppose "pigs can fly" is true, then two of the statements of { "pigs can't fly" , "pigs can fly"} are true. But we've already shown only one is true, hence $1=2$. Adding one to both sides gives $1+1=2+1=3$.
QED.