Is "p not implies q" logically equivalent to "not p implies q"?

Question

I am confused about whether $(A \not\rightarrow B)$ is logically equivalent to ~$(A \rightarrow B)$?

Answer 1

I would generally consider $p\not\to q$ to be an abbreviation for $\neg(p\to q)$, so they are equivalent by definition!

Note, however, that $\neg(p\to q)$ is not the same as $(\neg p)\to q$, and if you write $\neg p\to q$ it generally means the latter of these.