Definition of $\rightarrow$.

Question

Is the definition of $p\rightarrow q$ in logic $(\lnot p) \lor q$?

Answer 1

Yes . . . and no.

In classical logic, yes, $p\to q$ is defined (sometimes) as $(\lnot p)\lor q$. However, classical logic is not the only logic in town. Sometimes other symbols are used to indicate the difference, such as $p\supset q$, but such notation is also used for the material conditional, which is what is typically meant by $p\to q$.

So it depends.