Vacuously True

And statement true or false can be derived from a false hypothesis. If the hypothesis is false, then the conclusion can always be derived to be true or false (depending on what you argue).

Example: Every time I’ve played the lottery, ive won the jackpot (When they have never played to lottery).

Transclude of Drawing-2024-09-13-12.54.48.excalidraw

True Statements Follow From Anything

If you have a true statement $P$, then anything can imply $P$.

Proof

1. $P$
2. $P\vee \neg Q$ 1, addition law
3. $Q⟹P$ 2, conditional law