Final answer:
The correct counterexample for the statement that Carl will pass if he studies at least two hours for the test is option a) Carl studied one hour for the test and Carl did not pass.
Step-by-step explanation:
In this case, a counterexample is a statement that proves the original statement wrong.
a) If Carl studied one hour for the test and Carl did not pass, it shows that studying one hour is not sufficient to pass the test, contradicting the original statement. Therefore, this is a counterexample.
b) If Carl studied only 30 minutes and Carl passed the test, it shows that studying less than two hours can still result in passing, contradicting the original statement. Therefore, this is not a counterexample.
c) If Carl studied 3 hours for the test and Carl did not pass, it does not contradict the original statement that studying at least two hours will lead to passing. Therefore, this is not a counterexample.
d) If Carl studied for 2 hours and passed the test, it supports the original statement that studying at least two hours will lead to passing. Therefore, this is not a counterexample.
Based on these explanations, option a) Carl studied one hour for the test and Carl did not pass is the correct counterexample for the statement.