Express a boolean formula using only $\to$

Question

To express $F$ using only $\to$ for

$$F = \overline{A \lor B} = \overline{\overline{A} \to B}$$

but you only need to use $\to$. I do not know how to get rid of negation.

Answer 1

We need something like $\bot$ (tye constant that is always false) to write:

$¬A =_{def} A \to \bot$.

In boolean algebra we have the constants $0$ and $1$.

We have:

$x \to y= \overline x \lor y$.

Thus:

$x \to 0 = \overline x \lor 0 = \overline x$.