How does universal quantification apply to this equation?

Question

when I was reading a paper about the universal quantifier, I met this equation, says we can do conversions like the following:

A -> B ≡ ¬A v B

can anyone help me understand why this is an equation? Thanks

Answer 1

One way is with a truth table $$\begin {array} {c| c| c| c} A&B&A \implies B& \lnot A \vee B\\ \hline T&T&T&T \\ T&F&F&F\\F&T&T&T\\F&F&T&T\end {array}$$

Answer 2

It isn't necessarily read as an equation. In words it reads as this: A implies B is logically equivalent to not A or B

Answer 3

$(\neg (A\to B)\;)$ iff $\;(A$ is true AND $B$ is false $)\;$ iff $(A\land \neg B).$.... Therefore $(A\to B) \iff (\;\neg (\;\neg (A\to B)\;)\;)\iff$ $ (\;\neg (A\land \neg B)\;)\iff $ $(\;(\neg A)\lor \neg \neg B\;)\iff$ $\iff (\;(\neg A)\lor B\;).$