This problem appears to be dealing with conditionals and counterexamples in logic. A conditional statement generally takes the form "If $P$, then $Q$," where $P$ is the hypothesis and $Q$ is the conclusion. A counterexample shows that a conditional is false, meaning it shows an instance where the hypothesis is true but the conclusion is false.

For Emma to have found a counterexample, the conditional must be false. In logic, the only time a conditional statement "If $P$, then $Q$" is false is when $P$ (the hypothesis) is true, and $Q$ (the conclusion) is false.

So, the answer to the question would be:

• The truth value of the hypothesis is true.
• The truth value of the conclusion is false.

This is because a counterexample provides a specific case where the hypothesis holds true, but the conclusion does not, thereby disproving the conditional.

Do you need more explanation or clarification? Here are 5 follow-up questions to consider:

1. What is the general form of a conditional statement in logic?
2. Why does a conditional become false if the hypothesis is true and the conclusion is false?
3. Can a conditional be false if the hypothesis is false?
4. How would you represent a counterexample in symbolic logic?
5. Can there be multiple counterexamples to a conditional statement?

Tip: In logic, a counterexample only needs to disprove the conditional once to invalidate it—one true hypothesis and false conclusion suffices.