Final answer:
The inverse of the sentence "If Sam cooks, then I will not eat" is: If Sam does not cook, then I will eat.
Step-by-step explanation:
When finding the inverse of a conditional statement, we need to negate both the hypothesis and the conclusion, and then switch their positions. The inverse of the sentence "If Sam cooks, then I will not eat" is: If Sam does not cook, then I will eat. This is because the original statement says that if Sam cooks, then I will not eat. The inverse statement says that if Sam does not cook, then I will eat.