Final answer:
The correct answer is c) When p is a necessary condition for q. This means for q to be true, p must be true, but p alone does not guarantee the truth of q.
Step-by-step explanation:
When p is considered to be a criterion for q, it refers to the relationship where p is a necessary condition for q. This means that for q to be true, p must be true as well; however, p being true doesn't necessarily guarantee that q will be true. This relationship is the opposite of a sufficient condition, where if p is true, it guarantees that q is true as well. Therefore, the correct answer to the student's question is c) When p is a necessary condition for q.
To illustrate this with examples: being a bachelor is a sufficient condition for being unmarried because if one is a bachelor, it guarantees they are unmarried. However, being unmarried is a necessary condition for being a bachelor, but being unmarried alone doesn't guarantee one is a bachelor, as they could be divorced or widowed, for instance.