In a proposal, assume $p$ is the condition and $q$ the conclusion, so the proposal is $p \to q$.
Let $\neg$ be the negation on either condition or conclusion.
what is the name for the operation from $p\to q$ to $\neg p\to\neg q$? And what is the name for the operation from $p \to q$ to $p\to\neg q$? And from $p\to q$ to $\neg q\to\neg p$?
What topics in logic cover these stuffs?
In order to prove $p\to q$, is it equivalent to disprove $p\to\neg q$? Is this the so-called "proof by contradiction"? And is it equiv to prove $\neg q\to\neg p$?
Thanks and regards!