1. Let's first understand the problem: We want to create a counterexample for the implication $A \to B$. This means we want a case where $A$ is true but $B$ is false. 2. The implication $A \to B$ is logically equivalent to $\neg A \lor B$. It is false only when $A$ is true and $B$ is false. 3. To create a counterexample, we need to find specific statements or conditions for $A$ and $B$ such that $A$ holds but $B$ does not. 4. Example: Let $A$ be "It is raining" and $B$ be "The ground is wet". 5. Normally, if it is raining ($A$ true), the ground is wet ($B$ true), so $A \to B$ holds. 6. A counterexample would be a situation where it is raining ($A$ true) but the ground is not wet ($B$ false), for example, if the ground is covered by a waterproof roof. 7. Thus, the counterexample world is: $A$ = true (it is raining), $B$ = false (ground not wet). 8. This shows $A \to B$ is false in this world, proving the counterexample. Final answer: A counterexample to $A \to B$ is any scenario where $A$ is true and $B$ is false, such as raining but ground not wet due to a cover.