Why does false, false result in true ? As i stated. I do not love mathematics is not true is <=> i love mathematics. How could we explain that with logic ? Double negation ? could we say that saying false is the same thing as taking the negation ? and double-negation results in elimnation ? Please help and provide a good answer.
No you are getting a bit confused: if $p$ is false, the "$p$ is false" is another statement $q$, not $p$ itself. And clearly:
If $p$ is false, and you say "$p$ is false", then the statement "$p$ is false" is true, but $p$ is still false.
If you say "$p$ is false", and it turns out that this is wrong, then the statement "$p$ is false" is false, and $p$ is true$^1$.
"$p$" and "$p$ is false" are two diffeerent statements.
$^1$ (This is assuming that all statements are either true or false, as classical logic does; there are logics which assume more than two truth values or truth-value gaps.)