The statement $$A \to (B \to A)$$ is equivalent to:

We need to determine which statement is logically equivalent to $$A \to (B \to A)$$.

First, we simplify $$A \to (B \to A)$$. Since $$B \to A \equiv \neg B \vee A$$, we have $$A \to (B \to A) \equiv \neg A \vee (\neg B \vee A) \equiv (\neg A \vee A) \vee \neg B \equiv \text{True}$$.

So $$A \to (B \to A)$$ is a tautology (always true regardless of the truth values of $$A$$ and $$B$$).

Now we check the options. For $$A \to (A \vee B)$$: this equals $$\neg A \vee (A \vee B) \equiv (\neg A \vee A) \vee B \equiv \text{True}$$. This is also a tautology.

Since both $$A \to (B \to A)$$ and $$A \to (A \vee B)$$ are tautologies, they are logically equivalent (both are always true).

Therefore, $$A \to (B \to A)$$ is equivalent to $$A \to (A \vee B)$$.