7. (10 points) Use the rules of inference to show that the hypotheses imply the conclusion: If you eat carefully then you will have a healthy digestive system. If you exercise regularly you will be very fit. If you have a healthy digestive system or you are very fit, you will live to a ripe old age. You do not live to a ripe old age. Therefore, you did not eat carefully and you did not exercise regularly. Let c-"you eat carefully", h- "you have a healthy digestive system", e- "you excercise regularly" f- "you will be very fit, I-"you will live to a ripe old age" (a) (4 pts) Translate the hypotheses and conclusion to logical statements. (b) (8 pts) Construct a valid argument (justify each step) Hint: Remember you can also use the logical equivalences as a step in the aryument